Texas Instruments TI 84 User Guide
Texas Instruments TI 84 - Graphing Calculator, Programmable Manual
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- Texas Instruments TI 84 | User Guide - Page 1
TI-84 Plus TI-84 Plus Silver Edition Guidebook - Texas Instruments TI 84 | User Guide - Page 2
implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an "as-is" basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages - Texas Instruments TI 84 | User Guide - Page 3
frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications. However, there is no or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment. iii - Texas Instruments TI 84 | User Guide - Page 4
19, the full name TI-84 Plus Silver Edition is used to distinguish it from the TI-84 Plus. All the instructions and examples in this guidebook also work for the TI-84 Plus. All the functions of the TI-84 Plus Silver Edition and the TI-84 Plus are the same. The two graphing calculators differ only in - Texas Instruments TI 84 | User Guide - Page 5
Scientific - Scientific calculator keys access the capabilities of a standard scientific calculator. TI-84 Plus Graphing Keys Editing Keys Advanced Function Keys Scientific Calculator Keys Chapter 1: Operating the TI-84 Plus Silver Edition 2 - Texas Instruments TI 84 | User Guide - Page 6
TI-84 Plus are color-coded to help you easily locate the key you need. The light colored keys are the number keys. The light gray keys along the right side of the keyboard are the common math functions. The light gray keys across the top set up and display graphs the TI-84 Plus Silver Edition 3 - Texas Instruments TI 84 | User Guide - Page 7
84 Plus Turning On the Graphing Calculator To turn on the TI-84 Plus, press É. • If you previously had turned off the graphing calculator by pressing y M, the TI-84 Plus displays the home screen as it was when you last used it and clears any error. Chapter 1: Operating the TI-84 Plus Silver Edition - Texas Instruments TI 84 | User Guide - Page 8
Off the Graphing Calculator To turn off the TI-84 Plus manually, press y M. • All settings and memory contents are retained by Constant Memory™. • Any error condition is cleared. Batteries The TI-84 Plus uses five batteries: four AAA alkaline batteries and one SR44SW or 303 silver oxide backup - Texas Instruments TI 84 | User Guide - Page 9
0, the display may become completely blank. To restore the screen, press and release y, and then press and hold } until the display reappears. Chapter 1: Operating the TI-84 Plus Silver Edition 6 - Texas Instruments TI 84 | User Guide - Page 10
split screen to show graphs and text simultaneously. Home Screen The home screen is the primary screen of the TI-84 Plus. On this screen, enter instructions to execute and expressions to evaluate. The answers are displayed on the same screen. Chapter 1: Operating the TI-84 Plus Silver Edition 7 - Texas Instruments TI 84 | User Guide - Page 11
TI-84 Plus screen can display a maximum of 8 lines with a maximum of 16 characters per line. If all lines of the display are full, text scrolls off the top of the display. If an expression on the home screen, the Y= editor (Chapter 3), or the program 1: Operating the TI-84 Plus Silver Edition 8 - Texas Instruments TI 84 | User Guide - Page 12
ƒ during an insertion, the cursor becomes an underlined A (A). If you press y during an insertion, the underlined cursor becomes an underlined # (#). Graphs and editors sometimes display additional cursors, which are described in other chapters. Chapter 1: Operating the TI-84 Plus Silver Edition 9 - Texas Instruments TI 84 | User Guide - Page 13
you customize the appearance of your unit. To purchase additional faceplates, refer to the TI Online Store at education.ti.com. Removing a Faceplate 1. Lift the tab at the bottom edge of the faceplate away from the TI-84 Plus Silver Edition case. 2. Carefully lift the faceplate away from the unit - Texas Instruments TI 84 | User Guide - Page 14
Installing New Faceplates 1. Align the top of the faceplate in the corresponding grooves of the TI-84 Plus Silver Edition case. 2. Gently click the faceplate into place. Do not force. 3. Make sure you gently press each of the grooves to ensure the faceplate is installed - Texas Instruments TI 84 | User Guide - Page 15
| to highlight the time format you want. Press Í. 6. Press † to highlight HOUR. Press ' and type the hour. A number from 1-12 or 0-23. Chapter 1: Operating the TI-84 Plus Silver Edition 12 - Texas Instruments TI 84 | User Guide - Page 16
There are two options to turn the clock on. One option is through the MODE screen, the other is through the Catalog. Chapter 1: Operating the TI-84 Plus Silver Edition 13 - Texas Instruments TI 84 | User Guide - Page 17
1. Press y N. 2. Press † or } to scroll the CATALOG until the selection cursor points to ClockOff. 3. Press Í. ClockOff will turn off the Clock display. Chapter 1: Operating the TI-84 Plus Silver Edition 14 - Texas Instruments TI 84 | User Guide - Page 18
or a menu; do not spell it out. For example, to calculate the log of 45, you must press « 45. Do not enter the letters L, O, and G. If you enter LOG, the TI-84 Plus interprets the entry as implied multiplication of the variables L, O, and G. Chapter 1: Operating the TI-84 Plus Silver Edition 15 - Texas Instruments TI 84 | User Guide - Page 19
Calculate 3.76 P (L7.9 + ‡5) + 2 log 45. 3 Ë 76 ¥ £ Ì 7 Ë 9 Ã y C 5 ¤ ¤ Ã 2 « 45 ¤ Í Multiple Entries on a Line To enter two or more expressions or instructions on a line, separate them with colons (ƒ [:]). All instructions be one or two digits. Chapter 1: Operating the TI-84 Plus Silver Edition 16 - Texas Instruments TI 84 | User Guide - Page 20
a calculation or graph in progress, which is indicated by the busy indicator, press É. When you interrupt a calculation, a menu is displayed. • To return to the home screen, select 1:Quit. • To go to the location of the interruption, select 2:Goto. Chapter 1: Operating the TI-84 Plus Silver Edition - Texas Instruments TI 84 | User Guide - Page 21
return to the home screen, press ' or any nongraphing key. • To restart graphing, press a graphing key or select a graphing instruction. TI-84 Plus Edit Keys Keystrokes ~ or | } or † y | y ~ Í ' { insertion, press y 6 or press |, }, ~, or †. Chapter 1: Operating the TI-84 Plus Silver Edition 18 - Texas Instruments TI 84 | User Guide - Page 22
and interprets numbers and graphs. Mode settings are retained by the Constant Memory feature when the TI-84 Plus is turned off. All numbers, including elements of matrices and lists, are displayed according to the current mode settings. Chapter 1: Operating the TI-84 Plus Silver Edition 19 - Texas Instruments TI 84 | User Guide - Page 23
Radian Degree Unit of angle measure Func Par Pol Seq Type of graphing Connected Dot Whether to connect graph points Sequential Simul Whether to plot simultaneously Real a+bi re^qi to move the cursor to the setting you want. 3. Press Í. Chapter 1: Operating the TI-84 Plus Silver Edition 20 - Texas Instruments TI 84 | User Guide - Page 24
the mode as an instruction; for example, Func or Float. From a blank program command line, select the mode setting from the mode screen; the instruction is pasted to the than .001), the TI-84 Plus expresses the answer in scientific notation. Chapter 1: Operating the TI-84 Plus Silver Edition 21 - Texas Instruments TI 84 | User Guide - Page 25
TI-84 Plus interprets angle values in trigonometric functions and polar/rectangular conversions. Radian mode interprets angle values as radians. Answers display in radians. Degree mode interprets angle values as degrees. Answers display in degrees. Chapter 1: Operating the TI-84 Plus Silver Edition - Texas Instruments TI 84 | User Guide - Page 26
one function completely before the next function is evaluated and plotted. Simul (simultaneous) graphing-order mode evaluates and plots all selected functions for a single value of X and then evaluates and plots them for the next value of X. Chapter 1: Operating the TI-84 Plus Silver Edition 23 - Texas Instruments TI 84 | User Guide - Page 27
bottom half (Chapter 9). • G-T (graph-table) mode displays the current graph on the left half of the screen; it displays the table screen on the right half (Chapter 9). Set Clock Use the clock to set the time, date, and clock display formats. Chapter 1: Operating the TI-84 Plus Silver Edition 24 - Texas Instruments TI 84 | User Guide - Page 28
and complex numbers, matrices, lists, functions, stat plots, graph databases, graph pictures, and strings. The TI-84 Plus uses assigned names for variables and other items saved in , GDB0 Pic1, Pic2, ... , Pic9, Pic0 Str1, Str2, ... , Str9, Str0 Chapter 1: Operating the TI-84 Plus Silver Edition 25 - Texas Instruments TI 84 | User Guide - Page 29
applications.which are stored in Flash ROM. AppVars is a variable holder used to store variables created by independent applications. You cannot edit or change variables in AppVars unless you do so through the application which created them. Chapter 1: Operating the TI-84 Plus Silver Edition 26 - Texas Instruments TI 84 | User Guide - Page 30
of the variable at that time is used. To store a value to a variable from the home screen or a program using the ¿ key, begin on a blank line and follow these steps. 1. Enter the value you want to line on the home screen, and then press Í. Chapter 1: Operating the TI-84 Plus Silver Edition 27 - Texas Instruments TI 84 | User Guide - Page 31
Archive, Unarchive) You can archive data, programs, or other variables in a section of memory called user data archive where they cannot be edited or deleted inadvertently. Archived variables are and then the name of the variable or function. Chapter 1: Operating the TI-84 Plus Silver Edition 28 - Texas Instruments TI 84 | User Guide - Page 32
Entry) When you press Í on the home screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called ENTRY (last entry). When you turn off the TI-84 Plus, ENTRY is retained in memory. Chapter 1: Operating the TI-84 Plus Silver Edition 29 - Texas Instruments TI 84 | User Guide - Page 33
a single entry is more than 128 bytes, it is retained for ENTRY, but it cannot be placed in the ENTRY storage area. 1 ¿ƒ A Í 2 ¿ƒ B Í y [ Chapter 1: Operating the TI-84 Plus Silver Edition 30 - Texas Instruments TI 84 | User Guide - Page 34
N ¡ Í Í Í Multiple Entry Values on a Line To store to ENTRY two or more expressions or instructions, separate each expression or instruction with a colon, then press Í. All expressions and instructions separated by colons are stored in ENTRY. Chapter 1: Operating the TI-84 Plus Silver Edition 31 - Texas Instruments TI 84 | User Guide - Page 35
screen or from a program, the TI-84 Plus stores the answer to a storage area called Ans (last answer). Ans may be a real or complex number, a list, a matrix, or a string. When you turn off the TI-84 Plus, the value in Ans is retained in memory. Chapter 1: Operating the TI-84 Plus Silver Edition 32 - Texas Instruments TI 84 | User Guide - Page 36
line on the home screen, enter the function. The TI-84 Plus pastes the variable name Ans to the screen, then the function. 5 ¥ 2 Í ¯ 9 Ë 9 Í Storing Answers To store an answer, store Ans to a variable before you evaluate another expression. Chapter 1: Operating the TI-84 Plus Silver Edition 33 - Texas Instruments TI 84 | User Guide - Page 37
calculate the volume of a cylinder of radius 5 meters and height 3.3 meters, and then store the result in the variable V. yB5 ¡ Í ¯ 3 Ë 3 Í ¿ƒ V Í TI-84 Plus Menus Using a TI-84 Plus Menu You can access most TI-84 Plus editor when you select it. Chapter 1: Operating the TI-84 Plus Silver Edition 34 - Texas Instruments TI 84 | User Guide - Page 38
. The menu is displayed with the cursor on the first item. Displaying a Menu While using your TI-84 Plus, you often will need to access items from its menus. When you press a key that displays where you are working usually is displayed again. Chapter 1: Operating the TI-84 Plus Silver Edition 35 - Texas Instruments TI 84 | User Guide - Page 39
green arrows on the graphing calculator, between † and }, are the page-down and page-up symbols. To wrap to the last menu item directly from the first menu item, press }. To wrap to the first menu item directly from the last menu item, press †. Chapter 1: Operating the TI-84 Plus Silver Edition 36 - Texas Instruments TI 84 | User Guide - Page 40
q, press the key combination for that alpha character or q. If no items begin with that character, the cursor moves beyond it to the next item. Calculate 3‡27. 27 ¤ Í Chapter 1: Operating the TI-84 Plus Silver Edition 37 - Texas Instruments TI 84 | User Guide - Page 41
, and 5:Statistics each access more than one secondary menu. VARS Y-VARS 1: Window... 2: Zoom... X/Y, T/q, and U/V/W variables ZX/ZY, ZT/Zq, and ZU variables Chapter 1: Operating the TI-84 Plus Silver Edition 38 - Texas Instruments TI 84 | User Guide - Page 42
VARS Y-VARS 3: GDB... 4: Picture... 5: Statistics... 6: Table... 7: String... Graph database variables Picture variables XY, G, EQ, TEST, and PTS variables TABLE variables String VARS or VARS Y-VARS menu. • Press to display the VARS menu. Chapter 1: Operating the TI-84 Plus Silver Edition 39 - Texas Instruments TI 84 | User Guide - Page 43
in which functions in expressions are entered and evaluated on the TI-84 Plus. EOS lets you enter numbers and functions in a simple, ) and combinations (nCr) 5 Multiplication, implied multiplication, and division 6 Addition and subtraction Chapter 1: Operating the TI-84 Plus Silver Edition 40 - Texas Instruments TI 84 | User Guide - Page 44
1à(2...X) (Chapter 2). Parentheses All calculations inside a pair of parentheses are completed first. For example, in the expression 4(1+2), EOS first evaluates the portion inside the parentheses, 1+2, and then multiplies the answer, 3, by 4. Chapter 1: Operating the TI-84 Plus Silver Edition 41 - Texas Instruments TI 84 | User Guide - Page 45
also true for open parenthetical elements that precede the store or display-conversion instructions. Note: An open parenthesis following a list name, matrix name, or If you press ƒ A Ì ƒ B, it is interpreted as implied multiplication (A...MB). Chapter 1: Operating the TI-84 Plus Silver Edition 42 - Texas Instruments TI 84 | User Guide - Page 46
Features of the TI-84 Plus Flash - Electronic Upgradability The TI-84 Plus uses Flash technology, which lets you upgrade to future software versions without buying a new graphing calculator. As new functionality becomes available, you can electronically upgrade your TI-84 Plus from the Internet - Texas Instruments TI 84 | User Guide - Page 47
Other TI-84 Plus Features The TI-84 Plus guidebook that is included with your graphing calculator has introduced you to basic TI-84 Plus operations. This guidebook covers the other features and capabilities of the TI-84 Plus in greater detail. Chapter 1: Operating the TI-84 Plus Silver Edition 44 - Texas Instruments TI 84 | User Guide - Page 48
split the screen horizontally to display both a graph and a related editor (such as the Y= editor), the table, the stat list editor, or the home screen. Also, you can split the screen vertically to display a graph and its table simultaneously. Chapter 1: Operating the TI-84 Plus Silver Edition 45 - Texas Instruments TI 84 | User Guide - Page 49
for automatic computation. You can use lists to evaluate expressions at multiple values simultaneously and to graph a family of curves. For details, refer to: Chapter 11 Statistics You can perform definitions. For details, refer to: Chapter 12 Chapter 1: Operating the TI-84 Plus Silver Edition 46 - Texas Instruments TI 84 | User Guide - Page 50
the TI-84 Plus. You can paste any function or instruction from the CATALOG to the current cursor location. For details, refer to: Chapter 15 Programming You can enter and store programs that include extensive control and input/output instructions. Chapter 1: Operating the TI-84 Plus Silver Edition - Texas Instruments TI 84 | User Guide - Page 51
TI-84 Plus or TI-84 Plus Silver Edition. The TI-84 Plus also has an I/O port using an I/O unit-to-unit cable to communicate with a TI-84 Plus Silver Edition, a TI-84 Plus, a TI-83 Plus Silver Edition, a TI-83 Plus, a TI-83, a TI-82, a TI-73, CBL 2™, or a CBR™ System. With TI Connect™ software - Texas Instruments TI 84 | User Guide - Page 52
™ software and a USB computer cable to upgrade your TI-84 Plus. For details, refer to: Chapter 19 Error Conditions Diagnosing an Error The TI-84 Plus detects errors while performing these tasks. • Evaluating an expression • Executing an instruction • Plotting a graph • Storing a value When the TI-84 - Texas Instruments TI 84 | User Guide - Page 53
syntax error occurs in the contents of a Y= function during program execution, then the Goto option returns to the Y= editor, not to the program. Correcting an Error To correct an error, follow these steps. B. 4. Correct the expression. Chapter 1: Operating the TI-84 Plus Silver Edition 50 - Texas Instruments TI 84 | User Guide - Page 54
Chapter 2: Math, Angle, and Test Operations Getting Started: Coin Flip Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to model flipping a fair coin 10 times. You want to track how many of those 10 coin flips result in heads. You want to perform this - Texas Instruments TI 84 | User Guide - Page 55
3. Press ~ or | to view the additional counts in the list. Ellipses (...) indicate that the list continues Operations Using Lists with Math Operations Math operations that are valid for lists return a list calculated element by element. If you use two lists in the same expression, they must be - Texas Instruments TI 84 | User Guide - Page 56
, Subtraction, Multiplication, Division You can use + (addition, Ã), N (subtraction, ¹), ... (multiplication, ¯), and à (division, ¥) with real and complex numbers, expressions, lists, and matrices. You cannot use à with matrices. valueA+valueB valueA...valueB valueA N valueB valueA à - Texas Instruments TI 84 | User Guide - Page 57
Power, Square, Square Root You can use ^ (power, ›), 2 (square, ¡), and ‡( (square root, y C) with real and complex numbers, expressions, lists, and matrices. You cannot use ‡( with matrices. value^power È value2 ‡(value) È Inverse You can use L1 (inverse, œ) with real and complex numbers, - Texas Instruments TI 84 | User Guide - Page 58
numbers, expressions, and lists. e^(power) Constant e (constant, y [e]) is stored as a constant on the TI-84 Plus. Press y [e] to copy e to the cursor location. In calculations, the TI-84 Plus uses 2.718281828459 for e. Negation M (negation, Ì) returns the negative of value. You can use M with - Texas Instruments TI 84 | User Guide - Page 59
Note: On the TI-84 Plus, the negation symbol (M) is shorter and higher than the subtraction sign (N), which is displayed when you press ¹. Pi p (Pi, y B) is stored as a constant in the TI-84 Plus. In calculations, the TI-84 Plus uses 3.1415926535898 for p. Chapter 2: Math, Angle, and Test - Texas Instruments TI 84 | User Guide - Page 60
. 5: x‡ Calculates the xth root. 6: fMin( Finds the minimum of a function. 7: fMax( Finds the maximum of a function. 8: nDeriv( Computes the numerical derivative. 9: fnInt( Computes the function integral. 0: Solver... Displays the equation solver. 4Frac, 4Dec 4Frac (display as a fraction - Texas Instruments TI 84 | User Guide - Page 61
cannot be simplified or the resulting denominator is more than three digits, the decimal equivalent is returned. You can only use 4Frac following value. value 4Frac 4Dec (display as a decimal) displays an answer in decimal form. You can use 4Dec with real or complex numbers, expressions, lists, and - Texas Instruments TI 84 | User Guide - Page 62
x‡ (Root) x‡ (xth root) returns the xth root of value. You can use x‡ with real or complex numbers, expressions, and lists. xthrootx‡value fMin(, fMax( fMin( (function minimum) and fMax( (function maximum) return the value at which the local minimum or local maximum value of expression with respect - Texas Instruments TI 84 | User Guide - Page 63
As H becomes smaller, the approximation usually becomes more accurate. You can use nDeriv( once in expression. Because of the method used to calculate nDeriv(, the TI-84 Plus can return a false derivative value at a nondifferentiable point. Chapter 2: Math, Angle, and Test Operations 60 - Texas Instruments TI 84 | User Guide - Page 64
,lower,upper[,tolerance]) Note: To speed the drawing of integration graphs (when fnInt( is used in a Y= equation), increase the value of the Xres window variable before you press s. Using the Equation Solver Solver Solver displays the equation solver, in which you can solve for any variable in an - Texas Instruments TI 84 | User Guide - Page 65
Y= variable name from the VARS Y-VARS menu, and press Í. The expression is pasted to the equation solver. The expression is stored to the variable eqn as you enter it. 3. Press Í or †. The interactive solver editor is displayed. • The equation stored in eqn is set equal to zero and displayed on the - Texas Instruments TI 84 | User Guide - Page 66
to solve an equation such as K=.5MV2, enter eqn:0=KN.5MV2 in the equation editor. Entering and Editing Variable Values When you enter or edit a value for a variable in the interactive solver editor, the new value is stored in memory to that variable. You can enter an expression for a variable value - Texas Instruments TI 84 | User Guide - Page 67
steps. 1. Select 0:Solver from the MATH menu to display the interactive solver editor, if not already displayed. 2. Enter or edit the value of each known . Also, for equations with multiple roots, the TI-84 Plus will attempt to display the solution that is closest to your guess. Chapter - Texas Instruments TI 84 | User Guide - Page 68
The default guess is calculated as (---u---p----p---e---r----+-----l--o---w-----e---r--)- . 2 4. Edit bound={lower,upper}. lower and upper are the bounds between which the TI-84 Plus searches for a solution. This is optional, but it may help find the solution more quickly. The default is bound={L1â - Texas Instruments TI 84 | User Guide - Page 69
one or more variables. When you edit any variable value, the solid squares next to the previous solution and leftNrt=diff disappear. Move the cursor to the variable for which you now want to solve and press ƒ \. Controlling the Solution for Solver or solve( The TI-84 Plus solves equations through an - Texas Instruments TI 84 | User Guide - Page 70
The function solve( is available only from CATALOG or from within a program. It returns a solution (root) of expression for variable, given an initial guess, and lower and upper bounds within which the solution is sought. The default - Texas Instruments TI 84 | User Guide - Page 71
To display the MATH NUM menu, press ~. MATH NUM CPX PRB 1: abs( Absolute value 2: round( Round 3: iPart( Integer part 4: fPart( Fractional part 5: int( Greatest integer 6: min( Minimum value 7: max( Maximum value 8: lcm( Least common multiple 9: gcd( Greatest common divisor abs - Texas Instruments TI 84 | User Guide - Page 72
( (integer part) returns the integer part or parts of real or complex numbers, expressions, lists, and matrices. iPart(value) fPart( (fractional part) returns the fractional part or parts of real or complex numbers, expressions, lists, and matrices. Chapter 2: Math, Angle, and Test Operations 69 - Texas Instruments TI 84 | User Guide - Page 73
fPart(value) int( int( (greatest integer) returns the largest integer real or complex numbers, expressions, lists, and matrices. int(value) Note: For a given value, the result of int( is the same as the result of iPart( for nonnegative numbers and negative integers, but one integer less than the - Texas Instruments TI 84 | User Guide - Page 74
max( (maximum value) returns the larger of valueA and valueB or the largest element in list. If listA and listB are compared, max( returns a list of the larger of each pair of elements. If list and value are compared, max( compares each element in list with value. min(valueA,valueB) min(list) min( - Texas Instruments TI 84 | User Guide - Page 75
lcm(listA,listB) lcm(list,value) gcd(valueA,valueB) gcd(listA,listB) gcd(list,value) Entering and Using Complex Numbers Complex-Number Modes The TI-84 Plus displays complex numbers in rectangular form and polar form. To select a complex-number mode, press z, and then select either of the two modes - Texas Instruments TI 84 | User Guide - Page 76
are evaluated when the command is executed. Note about Radian Versus Degree Mode Radian mode is recommended for complex number calculations. Internally, the TI-84 Plus converts all entered trigonometric values to radians, but it does not convert values for exponential, logarithmic, or hyperbolic - Texas Instruments TI 84 | User Guide - Page 77
, including list elements, are displayed in either rectangular or polar form, as specified by the mode setting or by a display conversion instruction. In the example below, polar-complex (re^qi) and Radian modes are set. Rectangular-Complex Mode Rectangular-complex mode recognizes and displays - Texas Instruments TI 84 | User Guide - Page 78
Polar-Complex Mode Polar-complex mode recognizes and displays a complex number in the form re^qi, where r is the magnitude, e is the base of the natural log, q is the angle, and i is a constant equal to -1 . To enter a complex number in polar form, enter the value of r (magnitude), press y J ( - Texas Instruments TI 84 | User Guide - Page 79
MATH CPX (Complex) Operations MATH CPX Menu To display the MATH CPX menu, press ~ ~. MATH NUM CPX PRB 1: conj( Returns the complex conjugate. 2: real( Returns the real part. 3: imag( Returns the imaginary part. 4: angle( Returns the polar angle. 5: abs( Returns the magnitude (modulus). - Texas Instruments TI 84 | User Guide - Page 80
qi)) returns r†sin(q). angle( angle( returns the polar angle of a complex number or list of complex numbers, calculated as tanL1 (b/a), where b is the imaginary part and a is the real part. The calculation is adjusted by +p in the second quadrant or Np in the third quadrant. Chapter 2: Math, Angle - Texas Instruments TI 84 | User Guide - Page 81
angle(a+bi) returns tanL1(b/a). angle(re^(qi)) returns q, where Lp - Texas Instruments TI 84 | User Guide - Page 82
4Polar 4Polar (display as polar) displays a complex result in polar form. It is valid only at the end of an expression. It is not valid if the result is real. complex result8Polar returns re^(qi). MATH PRB (Probability) Operations MATH PRB Menu To display the MATH PRB menu, press |. MATH NUM - Texas Instruments TI 84 | User Guide - Page 83
rand in an expression. For example, rand5 generates a random number > 0 and < 5. With each rand execution, the TI-84 Plus generates the same random-number sequence for a given seed value. The TI-84 Plus factory-set seed value for rand is 0. To generate a different random-number sequence, store any - Texas Instruments TI 84 | User Guide - Page 84
reduced to either 0 or L1/2. At that point, the definition 0!=1 or the definition (L1à2)!=‡p is used to complete the calculation. Hence: n!=n...(nN1)...(nN2)... ... ...2...1, if n is an integer , 0 n!= n...(nN1)...(nN2)... ... ...1à2...‡p, if n+1à2 is an integer , 0 n! is an error, if neither n nor - Texas Instruments TI 84 | User Guide - Page 85
(The variable n equals value in the syntax description above.) randInt( randInt( (random integer) generates and displays a random integer within a range specified by lower and upper integer bounds. To generate a list of random numbers, specify an integer > 1 for numtrials (number of trials); if not - Texas Instruments TI 84 | User Guide - Page 86
of simulations); if not specified, the default is 1. randBin(numtrials,prob[,numsimulations]) Note: The seed value stored to rand also affects randInt(, randNorm(, and randBin( instructions. Chapter 2: Math, Angle, and Test Operations 83 - Texas Instruments TI 84 | User Guide - Page 87
ANGLE Menu To display the ANGLE menu, press y ;. The ANGLE menu displays angle indicators and instructions. The Radian/Degree mode setting affects the TI-84 Plus's interpretation of ANGLE menu entries. ANGLE 1: ¡ Degree notation 2: ' DMS minute notation 3: r Radian notation 4: 8DMS Displays - Texas Instruments TI 84 | User Guide - Page 88
For example, enter for 30 degrees, 1 minute, 23 seconds. If the angle mode is not set to Degree, you must use ¡ so that the TI-84 Plus can interpret the argument as degrees, minutes, and seconds. Degree mode Radian mode Degree ¡ (degree) designates an angle or list of angles as degrees, - Texas Instruments TI 84 | User Guide - Page 89
valuer Degree mode 8DMS 8DMS (degree/minute/second) displays answer in DMS format. The mode setting must be Degree for answer to be interpreted as degrees, minutes, and seconds. 8DMS is valid only at the end of a line. answer8DMS R8Pr (, R8Pq(, P8Rx(, P8Ry( R8Pr( converts rectangular coordinates - Texas Instruments TI 84 | User Guide - Page 90
R8Pr(x,y), R8Pq(x,y) Note: Radian mode is set. P8Rx( converts polar coordinates to rectangular coordinates and returns x. P8Ry( converts polar coordinates to rectangular coordinates and returns y. r and q can be lists. P8Rx(r,q), P8Ry(r,q) Note: Radian mode is set. Chapter 2: Math, Angle, and - Texas Instruments TI 84 | User Guide - Page 91
TEST (Relational) Operations TEST Menu To display the TEST menu, press y :. This operator... TEST LOGIC 1: = 2: ƒ 3: > 4: , 5: < 6: Returns 1 (true) if... Equal Not equal to Greater than Greater than or equal to Less than Less than or equal to Relational operators compare valueA and valueB - Texas Instruments TI 84 | User Guide - Page 92
operators are often used in programs to control program flow and in graphing to control the graph of a function over specific values 0. The TI-84 Plus performs the addition first because of EOS rules, and then it compares 4 to 5. • The expression 2+(2=2)+3 returns 6. The TI-84 Plus performs the - Texas Instruments TI 84 | User Guide - Page 93
). Only one value is zero (false). The value is zero (false). Boolean Operators Boolean operators are often used in programs to control program flow and in graphing to control the graph of the function over specific values. Values are interpreted as zero (false) or nonzero (true). and, or, xor and - Texas Instruments TI 84 | User Guide - Page 94
( returns 1 if value (which can be an expression) is 0. not(value) Using Boolean Operations Boolean logic is often used with relational tests. In the following program, the instructions store 4 into C. Chapter 2: Math, Angle, and Test Operations 91 - Texas Instruments TI 84 | User Guide - Page 95
On the TI-84 Plus, you can define one function in terms of another. To define Y2=LY1, press Ì to enter the negation sign. Press ~ to display the VARS Y-VARS menu. Then press Í to select 1:Function. The FUNCTION secondary menu is displayed. Press 1 to select 1:Y1. Chapter 3: Function Graphing 92 - Texas Instruments TI 84 | User Guide - Page 96
notice the new values for Xmin, Xmax, Ymin, and Ymax. Defining Graphs TI-84 Plus-Graphing Mode Similarities Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI-84 Plus graphing mode. Chapters 4, 5, and 6 describe aspects that are unique to parametric - Texas Instruments TI 84 | User Guide - Page 97
graph mode. 2. Press o and enter, edit, or select one or more functions in the Y= editor. 3. Deselect stat plots, if necessary. 4. Set the graph style TI-84 Plus tools described in this chapter. Saving a Graph for Later Use You can store the elements that define the current graph to any of 10 graph - Texas Instruments TI 84 | User Guide - Page 98
select Func mode before you enter values for the window variables and before you enter the functions. The TI-84 Plus has four graphing modes. • Func (function graphing) • Par (parametric graphing; Chapter 4) • Pol (polar graphing; Chapter 5) • Seq (sequence graphing; Chapter 6) Chapter 3: Function - Texas Instruments TI 84 | User Guide - Page 99
-order mode affects function plotting when more than one function is selected. Setting Modes from a Program To set the graphing mode and other modes from a program, begin on a blank line in the program editor and follow these steps. 1. Press z to display the mode settings. 2. Press †, ~, |, and } to - Texas Instruments TI 84 | User Guide - Page 100
2. Press † to move the cursor to the function you want to define or edit. To erase a function, press '. 3. Enter or edit the expression to define the function. • You may use functions and variables (including matrices Í or † to move the cursor to the next function. Chapter 3: Function Graphing 97 - Texas Instruments TI 84 | User Guide - Page 101
screen or program editor. 5. Press Í to complete the instruction. "expression"!Yn When the instruction is executed, the TI-84 Plus stores the expression to the designated variable Yn, selects the function, and displays the message Done. Evaluating Y= Functions in Expressions You can calculate the - Texas Instruments TI 84 | User Guide - Page 102
Y= editor. A function is selected when the = sign is highlighted. The TI-84 Plus graphs only the selected functions. You can select any or all functions Y1 through the selection status. When you enter or edit a function, it is selected automatically. When you clear a function, it is - Texas Instruments TI 84 | User Guide - Page 103
home screen or a program, begin on a blank line and follow these steps. 1. Press ~ to display the VARS Y-VARS menu. 2. Select 4:On/Off to display the ON/OFF secondary menu. 3. Select 1:FnOn to turn on one or more functions or 2:FnOff to turn off one or more functions. The instruction you select is - Texas Instruments TI 84 | User Guide - Page 104
. .,function n] 5. Press Í. When the instruction is executed, the status of each function in the Graph Styles for Functions MATH Graph Style Icons in the Y= Editor This table describes the graph styles available for function graphing. Use the styles to visually differentiate functions to be graphed - Texas Instruments TI 84 | User Guide - Page 105
Press o to display the Y= editor. 2. Press † and } to move the cursor to the function. 3. Press | | to move the cursor left, past the = sign, to the graph style icon in the first column. The insert cursor is displayed. (Steps 2 and 3 are interchangeable.) 4. Press Í repeatedly to rotate through the - Texas Instruments TI 84 | User Guide - Page 106
Shading Above and Below When you select é or ê for two or more functions, the TI-84 Plus rotates through four shading patterns. • Vertical lines shade the first function with a é or ê graph style. • Horizontal lines shade the second. • Negatively sloping diagonal lines shade the third. • Positively - Texas Instruments TI 84 | User Guide - Page 107
shading patterns rotate for each member of the family of curves. Setting a Graph Style from a Program To set the graph style from a program, select H:GraphStyle( from the PRGM CTL menu. To display this menu, press while in the program editor. function# is the number of the Y= function name in the - Texas Instruments TI 84 | User Guide - Page 108
Setting the Viewing Window Variables The TI-84 Plus Viewing Window The viewing window is the portion of the differ from one graphing mode to another. Xres sets pixel resolution (1 through 8) for function graphs only. The default is 1. • At Xres=1, functions are evaluated and graphed at each pixel - Texas Instruments TI 84 | User Guide - Page 109
to a specific digit, and then edit it. 3. Press Í, †, or }. If you entered an expression, the TI-84 Plus evaluates it. The new value is stored. Note: Xmin - Texas Instruments TI 84 | User Guide - Page 110
the instruction is executed, the TI-84 Plus stores the value to the window variable and displays the value. @X and @Y The variables @X and @Y (items 8 and 9 on the VARS (1:Window) X/Y secondary menu) define the distance from the center of one pixel to the center of any adjacent pixel on a graph - Texas Instruments TI 84 | User Guide - Page 111
off or on. ExprOn ExprOff Sets expression display on or off. Format settings define a graph's appearance on the display. Format settings apply to all graphing modes. Seq graphing mode has an additional mode setting (Chapter 6). Changing a Format Setting To change a format setting, follow these steps - Texas Instruments TI 84 | User Guide - Page 112
and q; if CoordOn format is selected, R and q are displayed. CoordOn, CoordOff CoordOn (coordinates on) displays the cursor coordinates at the bottom of the graph. If ExprOff format is selected, the function number is displayed in the top-right corner. CoordOff (coordinates off) does not display the - Texas Instruments TI 84 | User Guide - Page 113
is active. This format setting also applies to stat plots. When ExprOn is selected, the expression is displayed in the top-left corner of the graph screen. When ExprOff and CoordOn both are selected, the number in the top-right corner specifies which function is being traced. Chapter 3: Function - Texas Instruments TI 84 | User Guide - Page 114
, press s. TRACE, ZOOM instructions, and CALC operations display the graph automatically. As the TI-84 Plus plots the graph, the busy indicator is on. As the graph is plotted, X and Y are updated. Pausing or Stopping a Graph While plotting a graph, you can pause or stop graphing. • Press Í to pause - Texas Instruments TI 84 | User Guide - Page 115
of Curves If you enter a list (Chapter 11) as an element in an expression, the TI-84 Plus plots the function for each value in the list, thereby graphing a family of curves. In Simul graphingorder mode, it graphs all functions sequentially for the first element in each list, and then for the second - Texas Instruments TI 84 | User Guide - Page 116
than one list, the lists must have the same dimensions. Exploring Graphs with the Free-Moving Cursor Free-Moving Cursor When a graph is displayed, press |, ~, }, or † to move the cursor around the graph. When you first display the graph, no cursor is visible. When you press |, ~, }, or †, the cursor - Texas Instruments TI 84 | User Guide - Page 117
math coordinates, *accurate to within the width and height of the pixel. As Xmin, Xmax, Ymin, and Ymax get closer together (as in a Zoom In) graphing accuracy increases, and the coordinate values more closely approximate the math coordinates. Free- moving cursor "on" the curve Chapter 3: Function - Texas Instruments TI 84 | User Guide - Page 118
the next along a function. To begin a trace, press r. If the graph is not displayed already, press r to display it. The trace cursor is Í. press } or †. When the trace cursor moves along a function, the Y value is calculated from the X value; that is, Y=Yn(X). If the function is undefined at an X - Texas Instruments TI 84 | User Guide - Page 119
the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the X= prompt. The Chapter 3: Function Graphing 116 - Texas Instruments TI 84 | User Guide - Page 120
When you leave and return to TRACE, the trace cursor is displayed in the same location it was in when you left TRACE, unless Smart Graph has replotted the graph. Chapter 3: Function Graphing 117 - Texas Instruments TI 84 | User Guide - Page 121
on the first selected function. As you trace, the cursor coordinate values are updated. When you finish tracing the functions, press Í to resume program execution. Exploring Graphs with the ZOOM Instructions ZOOM Menu To display the ZOOM menu, press q. You can adjust the viewing window of the - Texas Instruments TI 84 | User Guide - Page 122
lists. Fits YMin and YMax between XMin and XMax. Zoom Cursor When you select 1:ZBox, 2:Zoom In, or 3:Zoom Out, the cursor on the graph becomes the zoom cursor (+), a smaller version of the free-moving cursor (+). ZBox To define a new viewing window using ZBox, follow these steps. 1. Select 1:ZBox - Texas Instruments TI 84 | User Guide - Page 123
In magnifies the part of the graph that surrounds the cursor location. Zoom Out displays a greater portion of the graph, centered on the cursor location. be the center of the new viewing window. 4. Press Í. The TI-83 Plus adjusts the viewing window by XFact and YFact; updates the window variables; - Texas Instruments TI 84 | User Guide - Page 124
point, move the cursor to the point that you want as the center of the new viewing window, and then press Í. To zoom out on a graph, select 3:Zoom Out and repeat steps 3 through 5. To cancel Zoom In or Zoom Out, press '. ZDecimal ZDecimal replots the functions immediately. It updates the window - Texas Instruments TI 84 | User Guide - Page 125
point that you want to be the center of the new window, and then press Í; ZInteger replots the functions. @X=1 @Y=1 Xscl=10 Yscl=10 Chapter 3: Function Graphing 122 - Texas Instruments TI 84 | User Guide - Page 126
4: SetFactors... Uses the previous viewing window. Stores the user-defined window. Recalls the user-defined window. Changes Zoom In and Zoom Out factors. Chapter 3: Function Graphing 123 - Texas Instruments TI 84 | User Guide - Page 127
user-defined viewing window. The userdefined viewing window is determined by the values stored with the ZoomSto instruction. The window variables are updated with the user-defined values, and the graph is plotted. ZOOM FACTORS The zoom factors, XFact and YFact, are positive numbers (not necessarily - Texas Instruments TI 84 | User Guide - Page 128
it. Using ZOOM MEMORY Menu Items from the Home Screen or a Program From the home screen or a program, you can store directly to any of the user-defined ZOOM variables. From a program, you can select the ZoomSto and ZoomRcl instructions from the ZOOM MEMORY menu. Chapter 3: Function Graphing 125 - Texas Instruments TI 84 | User Guide - Page 129
menu, press y /. Use the items on this menu to analyze the current graph functions. CALCULATE 1: value 2: zero 3: minimum 4: maximum 5: intersect 6: dy/dx 7: ‰f(x)dx Calculates a function Y value for a given X. Finds a zero (x-intercept) of a function. Finds a minimum of a function. Finds - Texas Instruments TI 84 | User Guide - Page 130
1. Select 1:value from the CALCULATE menu. The graph is displayed with X= in the bottom-left corner. 2. Enter a real value, which can be an expression, for X between Xmin and bounds and the accuracy of your guess. To find a zero of a function, follow these steps. Chapter 3: Function Graphing 127 - Texas Instruments TI 84 | User Guide - Page 131
1. Select 2:zero from the CALCULATE menu. The current graph is displayed with Left Bound? in to select the x-value for the left bound of the interval, and then press Í. A 4 indicator on the graph screen shows the left bound. Right Bound? is displayed in the bottom-left corner. Press | or ~ (or - Texas Instruments TI 84 | User Guide - Page 132
within a specified interval to a tolerance of 1âL5. To find a minimum or maximum, follow these steps. 1. Select 3:minimum or 4:maximum from the CALCULATE menu. The current graph is displayed. 2. Select the function and set left bound, right bound, and guess as described for zero. The cursor is on - Texas Instruments TI 84 | User Guide - Page 133
(slope) of a function at a point, with H=1âL3. To find a function's slope at a point, follow these steps. 1. Select 6:dy/dx from the CALCULATE menu. The current graph is displayed. 2. Press } or † to select the function for which you want to find the numerical derivative. Chapter 3: Function - Texas Instruments TI 84 | User Guide - Page 134
the fnInt( function, with a tolerance of H=1âL3. To find the numerical integral of a function, follow these steps. 1. Select 7:‰f(x)dx from the CALCULATE menu. The current graph is displayed with Lower Limit? in the bottom-left corner. 2. Press } or † to move the cursor to the function for which you - Texas Instruments TI 84 | User Guide - Page 135
integral value is displayed, and the integrated area is shaded. Note: The shaded area is a drawing. Use ClrDraw (Chapter 8) or any action that invokes Smart Graph to clear the shaded area. Chapter 3: Function - Texas Instruments TI 84 | User Guide - Page 136
Started is a fast-paced introduction. Read the chapter for details. Graph the parametric equation that describes the path of a ball hit at an The vertical and horizontal vectors of the ball's motion also will be graphed. Vertical vector: Horizontal vector: Gravity constant: X2(t)=0 X3(t)=X1(t) - Texas Instruments TI 84 | User Guide - Page 137
1. Press z. Press to select Par mode. Press to select Simul for simultaneous graphing of all three parametric equations in this example. 2. Press o. Press 30 „ ™ 25 y ; 1 (to select ¡) ¤ Í to define X1T the PARAMETRIC secondary menu. Press 2 Í to define Y2T. Chapter 4: Parametric Graphing 134 - Texas Instruments TI 84 | User Guide - Page 138
Y3T. 6. Press ~ 2, and then press 1 Í to define X3T. Press 0 Í to define Y3T. 7. Press | | } Í to change the graph style to è for X3T and Y3T. Press } Í Í to change the graph style to ë for X2T and Y2T. Press } Í Í to change the graph style to ë for X1T and Y1T. (These keystrokes assume that all - Texas Instruments TI 84 | User Guide - Page 139
and T (time) are displayed at the bottom of the screen. Defining and Displaying Parametric Graphs TI-84 Plus Graphing Mode Similarities The steps for defining a parametric graph are similar to the steps for defining a function graph. Chapter 4 assumes that you are familiar with Chapter 3: Function - Texas Instruments TI 84 | User Guide - Page 140
mode before you enter window variables and before you enter the components of parametric equations. Displaying the Parametric Y= Editor After selecting Par graphing mode, press o to display the parametric Y= editor. In this editor, you can display and enter both the X and Y components of up to - Texas Instruments TI 84 | User Guide - Page 141
3 for defining a function or editing a function. The independent variable in a parametric equation is T. In Par graphing mode, you can enter the define both of them. Selecting and Deselecting Parametric Equations The TI-84 Plus graphs only the selected parametric equations. In the Y= editor, - Texas Instruments TI 84 | User Guide - Page 142
change the T window variables. Setting the Graph Format To display the current graph format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings; Seq graphing mode has an additional axes format setting. Chapter 4: Parametric - Texas Instruments TI 84 | User Guide - Page 143
you press s, the TI-84 Plus plots the selected parametric equations. It evaluates the X and Y components for each value of T (from Tmin to Tmax in intervals of Tstep), and then plots each point defined by X and Y. The window variables define the viewing window. As the graph is plotted, X, Y, and - Texas Instruments TI 84 | User Guide - Page 144
• Select or deselect parametric equations. • Store values directly to window variables. Exploring Parametric Graphs Free-Moving Cursor The free-moving cursor in Par graphing works the same as in Func graphing. In RectGC format, moving the cursor updates the values of X and Y; if CoordOn format is - Texas Instruments TI 84 | User Guide - Page 145
is selected, R, q, and T are displayed. The X and Y (or R and q) values are calculated from T. To move five plotted points at a time on a function, press y | or y screen continue to change appropriately. Quick Zoom is available in Par graphing; panning is not. Moving the Trace Cursor to Any Valid T - Texas Instruments TI 84 | User Guide - Page 146
ZOOM secondary menu ZT/Zq items 1:ZTmin, 2:ZTmax, and 3:ZTstep are the zoom memory variables for Par graphing. CALC CALC operations in Par graphing work the same as in Func graphing. The CALCULATE menu items available in Par graphing are 1:value, 2:dy/dx, 3:dy/dt, and 4:dx/dt. Chapter 4: Parametric - Texas Instruments TI 84 | User Guide - Page 147
and then explore the appearance of the rose for other values of A and B. 1. Press z to display the MODE screen. Press to select Pol graphing mode. Select the defaults (the options on the left) for the other mode settings. 2. Press o to display the polar Y= editor. Press 8 ˜ 2.5 „ ¤ Í to define - Texas Instruments TI 84 | User Guide - Page 148
equation r1=Asin(Bq). Observe how the new values affect the graph. Defining and Displaying Polar Graphs TI-84 Plus Graphing Mode Similarities The steps for defining a polar graph are similar to the steps for defining a function graph. Chapter 5 assumes that you are familiar with Chapter 3: Function - Texas Instruments TI 84 | User Guide - Page 149
mode before you enter values for the window variables and before you enter polar equations. Displaying the Polar Y= Editor After selecting Pol graphing mode, press o to display the polar Y= editor. In this editor, you can enter and display up to six polar equations, r1 through r6. Each is - Texas Instruments TI 84 | User Guide - Page 150
3 for defining a function or editing a function. The independent variable in a polar equation is q. In Pol graphing mode, you can enter the polar variable q in either of two ways. • Press „. • Press ƒ [q]. Selecting and Deselecting Polar Equations The TI-84 Plus graphs only the selected polar - Texas Instruments TI 84 | User Guide - Page 151
format settings, press y .. Chapter 3 describes the format settings in detail. The other graphing modes share these format settings. Displaying a Graph When you press s, the TI-84 Plus plots the selected polar equations. It evaluates R for each value of q (from qmin to qmax in intervals of qstep - Texas Instruments TI 84 | User Guide - Page 152
Window Variables and Y.VARS Menus You can perform these actions from the home screen or a program. • Access functions by using the name of the equation as a variable. • Store polar equations. • Select or deselect polar equations. • Store values directly to window variables. - Texas Instruments TI 84 | User Guide - Page 153
; if CoordOn format is selected, R and q are displayed. TRACE To activate TRACE, press r. When TRACE is active, you can move the trace cursor along the graph of the equation one qstep at a time. When you begin a trace, the trace cursor is on the first selected function at qmin. If ExprOn format - Texas Instruments TI 84 | User Guide - Page 154
. The VARS ZOOM secondary menu ZT/Zq items 4:Zqmin, 5:Zqmax, and 6:Zqstep are zoom memory variables for Pol graphing. CALC CALC operations in Pol graphing work the same as in Func graphing. The CALCULATE menu items available in Pol graphing are 1:value, 2:dy/dx, and 3:dr/dq. Chapter 5: Polar - Texas Instruments TI 84 | User Guide - Page 155
Chapter 6: Sequence Graphing Getting Started: Forest and Trees Note: Getting Started is a fast-paced introduction. Read many years and with how many trees? 1. Press z. Press to select Seq graphing mode. 2. Press y . and select Time axes format and ExprOn format if necessary. Chapter 6: Sequence - Texas Instruments TI 84 | User Guide - Page 156
3. Press o. If the graph-style icon is not ç (dot), press | |, press Í until ç is displayed, and then press ~ ¤ to define the new trees. Press † 4000 to define the number of trees at the beginning of the program. 5. Press p 0 to set nMin=0. Press † 50 to set nMax=50. nMin and nMax evaluate forest - Texas Instruments TI 84 | User Guide - Page 157
you enter window variables and before you enter sequence functions. Sequence graphs automatically plot in Simul mode, regardless of the current plottingorder mode setting. TI-84 Plus Sequence Functions u, v, and w The TI-84 Plus has three sequence functions that you can enter from the keyboard - Texas Instruments TI 84 | User Guide - Page 158
In this editor, you can display and enter sequences for u(n), v(n), and w(n). Also, you can edit the value for nMin, which is the sequence window variable that defines the minimum n value to evaluate only with a recursive sequence, which requires an initial value. Chapter 6: Sequence Graphing 155 - Texas Instruments TI 84 | User Guide - Page 159
available for sequence graphing. Graph styles are ignored in Web format. Selecting and Deselecting Sequence Functions The TI-84 Plus graphs only the u(n) and its initial value u(nMin). Defining and Editing a Sequence Function To define or edit a sequence function, follow the steps in Chapter 3 - Texas Instruments TI 84 | User Guide - Page 160
u(5) directly, without first calculating u(1) or any previous term. The sequence equation above returns the sequence 2, 4, 6, 8, 10, ... for n = 1, 2, 3, 4, 5, ... . Note: You may leave blank the initial value u(nMin) when calculating nonrecursive sequences. Chapter 6: Sequence Graphing 157 - Texas Instruments TI 84 | User Guide - Page 161
below you cannot calculate u(5) without first calculating u(1), u(2), u(3), and u(4). Using an initial value u(nMin) = 1, the sequence above returns 1, 2, 4, 8, 16, ... . Note: On the TI-84 Plus, you must type specify initial values for the first two terms. Chapter 6: Sequence Graphing 158 - Texas Instruments TI 84 | User Guide - Page 162
u(n). Setting Window Variables To display the window variables, press p. These variables define the viewing window. The values below are defaults for Seq graphing in both Radian and Degree angle modes. nMin=1 nMax=10 PlotStart=1 PlotStep=1 Xmin=L10 Smallest n value to evaluate Largest n value to - Texas Instruments TI 84 | User Guide - Page 163
to begin with the fifth term in a sequence, for example, set PlotStart=5. The first four terms are evaluated but are not plotted on the graph. PlotStep is the incremental n value for graphing only. PlotStep does not affect sequence evaluation; it only designates which points are plotted on the - Texas Instruments TI 84 | User Guide - Page 164
3 describes the format settings in detail. The other graphing modes share these format settings. The axes setting on the Axes label display off or on Expression display on or off Setting Axes Format For sequence graphing, you can select from five axes formats. The table below shows the values that - Texas Instruments TI 84 | User Guide - Page 165
selected sequence functions, press s. As a graph is plotted, the TI-84 Plus updates X, Y, and n. Smart Graph applies to sequence graphs (Chapter 3). Exploring Sequence Graphs Free-Moving Cursor The free-moving cursor in Seq graphing works the same as in Func graphing. In RectGC format, moving the - Texas Instruments TI 84 | User Guide - Page 166
the number you entered are displayed in the bottom-left corner of the screen. You can enter an expression at the n= prompt. The Chapter 6: Sequence Graphing 163 - Texas Instruments TI 84 | User Guide - Page 167
for the current viewing window. When you have completed the entry, press Í to move the cursor. ZOOM ZOOM operations in Seq graphing work the same as in Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin, Ymax, and Yscl) window variables are affected. PlotStart, PlotStep, nMin, and nMax - Texas Instruments TI 84 | User Guide - Page 168
[w]. You can evaluate these names in any of three ways. • Calculate the nth value in a sequence. • Calculate a list of values in a sequence. • Generate a sequence with u(nstart,nstop[,nstep]). nstep is optional; default is 1. Graphing Web Plots Graphing a Web Plot To select Web axes format, press - Texas Instruments TI 84 | User Guide - Page 169
not u(nN2)). • It cannot reference n directly. • It cannot reference any defined sequence except itself. Displaying the Graph Screen In Web format, press s to display the graph screen. The TI-84 Plus: • Draws a y=x reference line in AxesOn format. • Plots the selected sequences with u(nN1) as the - Texas Instruments TI 84 | User Guide - Page 170
continue to press ~. Using Web Plots to Illustrate Convergence Example: Convergence 1. Press o in Seq mode to display the sequence Y= editor. Make sure the graph style is set to í (dot), and then define nMin, u(n) and u(nMin) as shown below. 2. Press y . Í to set Time axes format. 3. Press p and - Texas Instruments TI 84 | User Guide - Page 171
5. Press y . and select the Web axes setting. 6. Press p and change the variables below. Xmin=L10 Xmax=10 7. Press s to graph the sequence. 8. Press r, and then press ~ to draw the web. The displayed cursor coordinates n, X (u(nN1)), and Y (u(n)) change accordingly. When you press ~, a new n - Texas Instruments TI 84 | User Guide - Page 172
Phase Plots Graphing with uv, vw, and uw The phase-plot axes settings uv, vw, and uw show relationships between two sequences. To R = number of rabbits M = rabbit population growth rate without foxes K = rabbit population death rate with foxes (.05) (.001) Chapter 6: Sequence Graphing 169 - Texas Instruments TI 84 | User Guide - Page 173
Rn and Wn as shown below. Enter the sequence Rn as u(n) and enter the sequence Wn as v(n). 2. Press y . Í to select Time axes format. Chapter 6: Sequence Graphing 170 - Texas Instruments TI 84 | User Guide - Page 174
the variables as shown below. nMin=0 nMax=400 PlotStart=1 PlotStep=1 Xmin=0 Xmax=400 Xscl=100 Ymin=0 Ymax=300 Yscl=100 4. Press s to graph the sequence. 5. Press r ~ to individually trace the number of rabbits (u(n)) and foxes (v(n)) over time (n). Note: Press a number, and then press Í to jump - Texas Instruments TI 84 | User Guide - Page 175
Sequences and Window Variables Refer to the table if you are familiar with the TI-82. It shows TI-84 Plus sequences and sequence window variables, as well as their TI-82 counterparts. TI-84 Plus In the Y= editor: u(n) u(nMin) TI-82 Un UnStart (window variable) Chapter 6: Sequence Graphing 172 - Texas Instruments TI 84 | User Guide - Page 176
the table if you are familiar with the TI-82. It compares TI-84 Plus sequencename syntax and variable syntax with TI-82 sequence-name syntax and variable syntax. TI-84 Plus / TI-82 n / n u(n) / Un On TI-84 Plus, press: „ y [u] £ „ ¤ On TI-82, press: y ô y ó ¶¦À Chapter 6: Sequence Graphing 173 - Texas Instruments TI 84 | User Guide - Page 177
TI-84 Plus / TI-82 v(n) / Vn w(n) u(nN1) / UnN1 v(nN1) / VnN1 w(nN1) On TI-84 Plus, press: y [v] £ „ ¤ y [w] £ „ ¤ y [u y [v y [w On TI-82, press: y ó ¶¦Á not available y õ y ö not available Chapter 6: Sequence Graphing 174 - Texas Instruments TI 84 | User Guide - Page 178
the function Y = X3 N 2X at each integer between L10 and 10. How many sign changes occur, and at what X values? 1. Press z to set Func graphing mode. 2. Press o. Press „ 3 to select 3. Then press ¹ 2 „ to enter the function Y1=X3N2X. 3. Press y - to display the TABLE SETUP screen. Press Ì 10 Í to - Texas Instruments TI 84 | User Guide - Page 179
Press Í to select Indpnt: Auto (automatically generated independent values). Press † Í to select Depend: Auto (automatically generated dependent values). 4. Press y 0 to display the table screen. 5. Press † until you see the sign changes in the value of Y1. How many sign changes occur, and at what X - Texas Instruments TI 84 | User Guide - Page 180
-variable columns. The table is empty; when you enter a value for the independent variable, all corresponding dependent-variable values are calculated and displayed automatically. Values are displayed automatically for the independent variable; to generate a value for a dependent variable, move the - Texas Instruments TI 84 | User Guide - Page 181
in the current table. When you press y - in the program editor, you can select IndpntAuto, IndpntAsk, DependAuto, and DependAsk. graphing mode is used. In Par mode, you must define both components of each parametric equation (Chapter 4). Editing Dependent Variables from the Table Editor To edit - Texas Instruments TI 84 | User Guide - Page 182
3. Press Í. The cursor moves to the bottom line. Edit the function. 4. Press Í or †. The new values are calculated. The table and the Y= function are updated automatically. Note: You also can use this feature to view the function that defines a dependent variable without having - Texas Instruments TI 84 | User Guide - Page 183
in the first column Dependent-variable values in the second and third columns Current cell's full value Independent and Dependent Variables The current graphing mode determines which independent and dependent variables are displayed in the table (Chapter 1). In the table above, for example, the - Texas Instruments TI 84 | User Guide - Page 184
dependent variables Y1 and Y2 are displayed because Func graphing mode is set. Graphing Mode Func (function) Par (parametric) Pol ( Home Screen or a Program From the home screen, select the ClrTable instruction from the CATALOG. To clear the table, press Í. From a program, select 9:ClrTable from - Texas Instruments TI 84 | User Guide - Page 185
. Press ~ or | to display dependent variables defined by other selected Y= functions. The independent variable always remains in the left column, except during a trace with Par graphing mode and G-T split-screen mode set. Chapter 7: Tables 182 - Texas Instruments TI 84 | User Guide - Page 186
Note: To simultaneously display two dependent variables on the table that are not defined as consecutive Y= functions, go to the Y= editor and deselect the Y= functions between the two you want to display. For example, to simultaneously display Y4 and Y7 on the table, go to the Y= editor and - Texas Instruments TI 84 | User Guide - Page 187
Chapter 8: Draw Instructions Getting Started: Drawing a Tangent Line Getting Started is a fast-paced introduction. Read to display the Y= editor. Press ˜ „ ¤ to store sin(X) in Y1. 2. Press q 7 to select 7:ZTrig, which graphs the equation in the Zoom Trig window. Chapter 8: Draw Instructions 184 - Texas Instruments TI 84 | User Guide - Page 188
3. Press y < 5 to select 5:Tangent(. The tangent instruction is initiated. 4. Press y C 2 ¤ ¥ 2. 5. Press Í. The tangent line is drawn; the X value and the tangent-line equation are displayed on the graph. Chapter 8: Draw Instructions 185 - Texas Instruments TI 84 | User Guide - Page 189
the DRAW Menu DRAW Menu To display the DRAW menu, press y - Texas Instruments TI 84 | User Guide - Page 190
y-coordinate values. You can use most DRAW menu and DRAW POINTS menu instructions to draw directly on a graph, using the cursor to identify the coordinates. You also can execute these instructions from the home screen or from within a program. If a graph is not displayed when you select a DRAW menu - Texas Instruments TI 84 | User Guide - Page 191
drawn elements. Clearing Drawings from the Home Screen or a Program To clear drawings on a graph from the home screen or a program, begin on a blank line on the home screen or in the program editor. Select 1:ClrDraw from the DRAW menu. The instruction is copied to the cursor location. Press Í. When - Texas Instruments TI 84 | User Guide - Page 192
Segments Drawing a Line Segment Directly on a Graph To draw a line segment when a graph is displayed, follow these steps. 1. Select 3. To cancel Line(, press '. Drawing a Line Segment from the Home Screen or a Program Line( also draws a line segment between the coordinates (X1,Y1) and (X2,Y2). The - Texas Instruments TI 84 | User Guide - Page 193
Y1,X2,Y2,0) Drawing Horizontal and Vertical Lines Drawing a Line Directly on a Graph To draw a horizontal or vertical line when a graph is displayed, follow these steps. 1. Select 3:Horizontal or 4:Vertical from the ) through which you want the drawn line to pass. Chapter 8: Draw Instructions 190 - Texas Instruments TI 84 | User Guide - Page 194
from the Home Screen or a Program Horizontal (horizontal line) draws a horizontal line at Y=y. y can be an expression but not a list. Horizontal y Vertical (vertical line) draws a vertical line at X=x. x can be an expression but not a list. Vertical x To instruct the TI-84 Plus to draw more than one - Texas Instruments TI 84 | User Guide - Page 195
Press † and } to move the cursor to the function for which you want to draw the tangent line. The current graph's Y= function is displayed in the top-left corner, if ExprOn is selected. 3. Press ~ and | or enter a number other modes, the dy/dx value is displayed. Chapter 8: Draw Instructions 192 - Texas Instruments TI 84 | User Guide - Page 196
on the mode screen if you want to see fewer digits displayed for X and the equation for Y. Drawing a Tangent Line from the Home Screen or a Program Tangent( (tangent line) draws a line tangent to expression in terms of X, such as Y1 or X2, at point X=value. X can be an expression. expression is - Texas Instruments TI 84 | User Guide - Page 197
X on the current graph. When you select 6:DrawF from the DRAW menu, the TI-84 Plus returns to the home screen or the program editor. DrawF is TI-84 Plus returns to the home screen or the program editor. DrawInv is not interactive. DrawInv works in Func mode only. Chapter 8: Draw Instructions 194 - Texas Instruments TI 84 | User Guide - Page 198
use a list in expression to draw a family of curves. Shading Areas on a Graph Shading a Graph To shade an area on a graph, select 7:Shade( from the DRAW menu. The instruction is pasted to the home screen or to the program editor. Shade( draws lowerfunc and upperfunc in terms of X on the current - Texas Instruments TI 84 | User Guide - Page 199
shades every fifth pixel shades every sixth pixel shades every seventh pixel shades every eighth pixel Shade(lowerfunc,upperfunc[,Xleft,Xright,pattern,patres]) Chapter 8: Draw Instructions 196 - Texas Instruments TI 84 | User Guide - Page 200
. Press Í to draw the circle on the graph. Note: This circle is displayed as circular, regardless of the window variable values, because you drew it directly on the display. When you use the Circle( instruction from the home screen or a program, the current window variables may distort the shape - Texas Instruments TI 84 | User Guide - Page 201
want the text to begin. 3. Enter the characters. Press ƒ or y 7 to enter letters and q. You may enter TI-84 Plus functions, variables, and instructions. The font is proportional, so the exact number of characters you can place on the graph varies. As you type, the characters are placed on top of the - Texas Instruments TI 84 | User Guide - Page 202
from the Home Screen or a Program Text( places on the current graph the characters comprising value, which can include TI-84 Plus functions and instructions. The top-left corner of the first character is at pixel (row,column), where row is an integer between 0 and 57 and column is an - Texas Instruments TI 84 | User Guide - Page 203
Graph Using Pen to Draw on a Graph Pen draws directly on a graph only. You cannot execute Pen from the home screen or a program. To draw on a displayed graph local minimum of the selected function. Note: To continue drawing on the graph, move the cursor to a new position where you want to begin drawing - Texas Instruments TI 84 | User Guide - Page 204
DRAW POINTS Menu To display the DRAW POINTS menu, press y < ~. The TI-84 Plus's interpretation of these instructions depends on whether you accessed this menu from the home screen or the program editor or directly from a graph. DRAW POINTS 1: Pt-On( 2: Pt-Off( 3: Pt-Change( 4: Pxl-On( 5: Pxl-Off - Texas Instruments TI 84 | User Guide - Page 205
3. To cancel Pt-On(, press '. Erasing Points with Pt-Off( To erase (turn off) a drawn point on a graph, follow these steps. 1. Select 2:Pt-Off( (point off) from the DRAW POINTS menu. 2. Move the cursor to the , repeat steps 2 and 3. To cancel Pt-Change(, press '. Chapter 8: Draw Instructions 202 - Texas Instruments TI 84 | User Guide - Page 206
-84 Plus Pixels A pixel is a square dot on the TI-84 Plus display. The Pxl- (pixel) instructions let you turn on, turn off, or reverse a pixel (dot) on the graph using the cursor. When you select a pixel instruction from the DRAW POINTS menu, the TI-84 Plus returns to the home screen or the program - Texas Instruments TI 84 | User Guide - Page 207
-Test( pxl-Test( (pixel test) returns 1 if the pixel at (row,column) is turned on or 0 if the pixel is turned off on the current graph. row must be an integer between 0 and 62. column must be an integer between 0 and 94. pxl-Test(row,column) Chapter 8: Draw - Texas Instruments TI 84 | User Guide - Page 208
Menu To display the DRAW STO menu, press y < |. When you select an instruction from the DRAW STO menu, the TI-84 Plus returns to the home screen or the program editor. The picture and graph database instructions are not interactive. DRAW POINTS STO 1: StorePic 2: RecallPic 3: StoreGDB 4: RecallGDB - Texas Instruments TI 84 | User Guide - Page 209
TI-84 Plus will store the picture to Pic3. Note: You also can select a variable from the PICTURE secondary menu ( 4). The variable is pasted next to StorePic. 3. Press Í to display the current graph and store the picture. Recalling Graph Pictures (Pic) Recalling a Graph Picture To recall a graph - Texas Instruments TI 84 | User Guide - Page 210
a picture. For example, if you enter 3, the TI-84 Plus will recall the picture stored to Pic3. Note: You also can select a variable from the PICTURE secondary menu ( 4). The variable is pasted next to RecallPic. 3. Press Í to display the current graph with the picture superimposed on it. Note - Texas Instruments TI 84 | User Guide - Page 211
current cursor location. 2. Enter the number (from 1 to 9, or 0) of the GDB variable to which you want to store the graph database. For example, if you enter 7, the TI-84 Plus will store the GDB to GDB7. Note: You also can select a variable from the GDB secondary menu ( 3). The variable is pasted - Texas Instruments TI 84 | User Guide - Page 212
replace the current GDB with the recalled GDB. The new graph is not plotted. The TI-84 Plus changes the graphing mode automatically, if necessary. Deleting a Graph Database To delete a GDB from memory, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18). Chapter 8: Draw Instructions 209 - Texas Instruments TI 84 | User Guide - Page 213
Chapter 8: Draw Instructions 210 - Texas Instruments TI 84 | User Guide - Page 214
45¡, 60¡, 90¡, and so on. 1. Press z to display the mode screen. Press to select Degree mode. Press † ~ Í to select Par (parametric) graphing mode. Press to select G-T (graphtable) split-screen mode. 2. Press y . to display the format screen. Press to select ExprOff. Chapter 9: Split Screen 211 - Texas Instruments TI 84 | User Guide - Page 215
On the left, the unit circle is graphed parametrically in Degree mode and the trace cursor is activated. When T=0 (from the graph trace coordinates), you can see from . Press † or } to highlight a value you want to edit, and then enter a new value directly in the table to overwrite the previous value. - Texas Instruments TI 84 | User Guide - Page 216
to the next-to-last line on the mode screen. • Select Horiz (horizontal) to display the graph screen and another screen split horizontally. • Select G-T (graph-table) to display the graph screen and table screen split vertically. $ $ The split screen is activated when you press any key that - Texas Instruments TI 84 | User Guide - Page 217
graphs. Press y 0 to make the table portion of the split screen active and to display the list data. Press † or } to highlight a value you want to edit in which the graph is displayed. If you press y 0, the cursor is placed in the half in which the table is displayed. The TI-84 Plus will remain in - Texas Instruments TI 84 | User Guide - Page 218
Horiz Mode In Horiz (horizontal) split-screen mode, a horizontal line splits the screen into top and bottom halves. The top half displays the graph. The bottom half displays any of these editors. • Home screen (four lines) • Y= editor (four lines) • Stat list editor (two rows) • Window editor - Texas Instruments TI 84 | User Guide - Page 219
screen when in Horiz mode, press any key or key combination that displays the graph, home screen, Y= editor, stat list editor, window editor, or table editor. G-T (Graph-Table) Split Screen G-T Mode In G-T (graph-table) split-screen mode, a vertical line splits the screen into left and right halves - Texas Instruments TI 84 | User Guide - Page 220
, press y 0. If the values at the right are list data, these values can be edited similarly to using the Stat List Editor. Using TRACE in G-T Mode As you press | or ~ to move the trace cursor along a graph in the split screen's left half in G-T mode, the table on the right half automatically - Texas Instruments TI 84 | User Guide - Page 221
screens in G-T splitscreen mode. To return to the G-T split screen from a full screen when in G-T mode, press any key or key combination that displays the graph or the table. TI-84 Plus Pixels in Horiz and G-T Modes TI-84 Plus Pixels in Horiz and G-T Modes Chapter 9: Split Screen 218 - Texas Instruments TI 84 | User Guide - Page 222
be {25; column must be {94. • In G-T mode, row must be {45; column must be {46. Text(row,column,"text") PRGM I/O Menu Output( Instruction For the Output( instruction: • In Horiz mode, row must be {4; column must be {16. • In G-T mode, row must be {8; column must be {16. Chapter 9: Split Screen 219 - Texas Instruments TI 84 | User Guide - Page 223
these steps. 1. Press z while the cursor is on a blank line in the program editor. 2. Select Horiz or G-T. The instruction is pasted to the cursor location. The mode is set when the instruction is encountered during program execution. It remains in effect after execution. Note: You also can paste - Texas Instruments TI 84 | User Guide - Page 224
and 2X + 3Y + 4Z = 3. On the TI-84 Plus, you can solve a system of linear equations by entering the coefficients as elements in a matrix, and then using rref( to obtain the reduced row-echelon form. 1. Press y . Press ~ ~ to display the MATRX EDIT menu. Press 1 to select 1: [A]. 2. Press 2 Í 4 Í to - Texas Instruments TI 84 | User Guide - Page 225
= L3 + Z Y = 3 N 2Z Defining a Matrix What Is a Matrix? A matrix is a two-dimensional array. You can display, define, or edit a matrix in the matrix editor. The TI-84 Plus has 10 matrix variables, [A] through [J]. You can define a matrix directly in an expression. A matrix, depending on available - Texas Instruments TI 84 | User Guide - Page 226
2. Select the matrix you want to define. The MATRX EDIT screen is displayed. Accepting or Changing Matrix Dimensions The dimensions matrix are 1 × 1. You must accept or change the dimensions each time you edit a matrix. When you select a matrix to define, the cursor highlights the row dimension - Texas Instruments TI 84 | User Guide - Page 227
matrix elements. In a new matrix, all values are zero. Select the matrix from the MATRX EDIT menu and enter or accept the dimensions. The center portion of the matrix editor displays up to 4 matrix. Ellipses in the left or right column indicate additional columns. # or $ in the right column indicate - Texas Instruments TI 84 | User Guide - Page 228
a Matrix To delete matrices from memory, use the MEMORY MANAGEMENT/DELETE secondary menu (Chapter 18). Viewing a Matrix The matrix editor has two contexts, viewing and editing. In viewing context, you can use the cursor keys to move quickly from one matrix element to the next. The full value of the - Texas Instruments TI 84 | User Guide - Page 229
context by pressing Í, ', or an entry key. 4. Change the value of the matrix element using the editing-context keys described below. You may enter an expression, which is evaluated when you leave editing context. Note: You can press ' Í to restore the value at the rectangular cursor if you make - Texas Instruments TI 84 | User Guide - Page 230
or ~ † or } Í ' Any entry character y 6 { Function Moves the edit cursor within the value Stores the value displayed on the bottom line to the matrix bottom line Copies the character to the location of the edit cursor on the bottom line Activates the insert cursor Deletes the character under the - Texas Instruments TI 84 | User Guide - Page 231
contents of the matrix into the expression with y K (Chapter 1). • Enter the matrix directly (see below). Entering a Matrix in an Expression You can enter, edit, and store a matrix in the matrix editor. You also can enter a matrix directly in an expression. To enter a matrix in an expression, follow - Texas Instruments TI 84 | User Guide - Page 232
of a matrix on the home screen, select the matrix from the MATRX NAMES menu, and then press Í. Ellipses in the left or right column indicate additional columns. # or $ in the right column indicate additional rows. Press ~, |, †, and } to scroll the matrix. Chapter 10: Matrices 229 - Texas Instruments TI 84 | User Guide - Page 233
the existing matrix. 5. Press Í to copy the matrix to the new matrix name. Accessing a Matrix Element On the home screen or from within a program, you can store a value to, or recall a value from, a matrix element. The element must be within the currently defined matrix dimensions. Select matrix - Texas Instruments TI 84 | User Guide - Page 234
of the math functions on the TI-84 Plus keyboard, the MATH menu, the MATH NUM menu, and the MATH TEST menu with matrices. However, the dimensions must be appropriate. Each of the functions below creates a new matrix; the original matrix remains the same. Addition, Subtraction, Multiplication To add - Texas Instruments TI 84 | User Guide - Page 235
matrixA...matrixB Multiplying a matrix by a value or a value by a matrix returns a matrix in which each element of matrix is multiplied by value. matrix...value value...matrix Negation Negating a matrix (Ì) returns a matrix in which the sign of every element is changed (reversed). Lmatrix Chapter - Texas Instruments TI 84 | User Guide - Page 236
abs( abs( (absolute value, MATH NUM menu) returns a matrix containing the absolute value of each element of matrix. abs(matrix) round( round( (MATH NUM menu) returns a matrix. It rounds every element in matrix to #decimals ( 9). If #decimals is omitted, the elements are rounded to 10 digits. round - Texas Instruments TI 84 | User Guide - Page 237
matrixL1 Powers To raise a matrix to a power, matrix must be square. You can use 2 (¡), 3 (MATH menu), or ^power (›) for integer power between 0 and 255. matrix2 matrix3 matrix^power Relational Operations To compare two matrices using the relational operations = and ƒ (TEST menu), they must have - Texas Instruments TI 84 | User Guide - Page 238
ƒmatrixB returns 1 if at least one comparison is false; it returns 0 if no comparison is false. iPart(, fPart(, int( iPart( (integer part), fPart( (fractional part), and int( (greatest integer) are on the MATH NUM menu. iPart( returns a matrix containing the integer part of each element of matrix - Texas Instruments TI 84 | User Guide - Page 239
(matrix) Using the MATRX MATH Operations MATRX MATH Menu To display the MATRX MATH menu, press y ~. NAMES MATH EDIT 1: det( Calculates the determinant. 2: T Transposes the matrix. 3: dim( Returns the matrix dimensions. 4: Fill( Fills all elements with a constant. 5: identity( Returns - Texas Instruments TI 84 | User Guide - Page 240
NAMES MATH EDIT 9: List4matr( Stores a list to a matrix. 0: cumSum( Returns the cumulative sums of a matrix. A: ref( Returns the row-echelon form of a matrix. B: rref( Returns the reduced row- - Texas Instruments TI 84 | User Guide - Page 241
matrixT Accessing Matrix Dimensions with dim( dim( (dimension) returns a list containing the dimensions ({rows columns}) of matrix. dim(matrix) Note: dim(matrix)"Ln:Ln(1) returns the number of rows. dim(matrix)"Ln:Ln(2) returns the number of columns. Creating a Matrix with dim( Use dim( with ¿ to - Texas Instruments TI 84 | User Guide - Page 242
an existing matrixname to dimensions rows × columns. The elements in the old matrixname that are within the new dimensions are not changed. Additional created elements are zeros. Matrix elements that are outside the new dimensions are deleted. {rows,columns}"dim(matrixname) Fill( Fill( stores value - Texas Instruments TI 84 | User Guide - Page 243
identity(dimension) randM( randM( (create random matrix) returns a rows × columns random matrix of integers , L9 and 9. The seed value stored to the rand function controls the values (Chapter 2). randM(rows,columns) augment( augment( appends matrixA to matrixB as new columns. matrixA and matrixB - Texas Instruments TI 84 | User Guide - Page 244
Matr4list( (matrix stored to list) fills each listname with elements from each column in matrix. Matr4list( ignores extra listname arguments. Likewise, Matr4list( ignores extra matrix columns. Matr4list(matrix,listnameA,...,listname n) Matr4list( also fills a listname with elements from a specified - Texas Instruments TI 84 | User Guide - Page 245
List4matr(listA,...,list n,matrixname) cumSum( cumSum( returns cumulative sums of the elements in matrix, starting with the first element. Each element is the cumulative sum of the column from top to bottom. cumSum(matrix) Row Operations MATRX MATH menu items A through F are row operations. You - Texas Instruments TI 84 | User Guide - Page 246
ref(, rref( ref( (row-echelon form) returns the row-echelon form of a real matrix. The number of columns must be greater than or equal to the number of rows. ref(matrix) rref( (reduced row-echelon form) returns the reduced row-echelon form of a real matrix. The number of columns must be greater than - Texas Instruments TI 84 | User Guide - Page 247
) returns a matrix. It multiplies row of matrix by value and stores the results in row. ...row(value,matrix,row) ...row+( ...row+( (row multiplication and addition) returns a matrix. It multiplies rowA of matrix by value, adds it to rowB, and stores the results in rowB. Chapter 10: Matrices 244 - Texas Instruments TI 84 | User Guide - Page 248
...row+(value,matrix,rowA,rowB) Chapter 10: Matrices 245 - Texas Instruments TI 84 | User Guide - Page 249
Generating a Sequence Getting Started is a fast-paced introduction. Read the chapter for details. Calculate the first eight terms of the sequence 1/A2. Store the results to a user-created list. Then display the results in fraction form. Begin this example on a blank line on the home screen. 1. Press - Texas Instruments TI 84 | User Guide - Page 250
4Frac to the current cursor location. 8. Press Í to show the sequence in fraction form. Press ~ repeatedly (or press and hold ~) to scroll the list and view all the list elements. Naming Lists Using TI-84 Plus List Names L1 through L6 The TI-84 Plus has six list names in memory: L1, L2, L3, L4, L5 - Texas Instruments TI 84 | User Guide - Page 251
Creating a List Name on the Home Screen To create a list name on the home screen, follow these steps. 1. Press y E, enter one or more list elements, and then press y F. Separate list elements with commas. List elements can be real numbers, complex numbers, or expressions. 2. Press ¿. 3. Press ƒ [ - Texas Instruments TI 84 | User Guide - Page 252
:, Freq2:, XList:, or YList: prompt in the inferential stat editors • On the home screen using SetUpEditor You can create as many list names as your TI-84 Plus memory has space to store. Storing and Displaying Lists Storing Elements to a List You can store list elements in either of two ways. • Use - Texas Instruments TI 84 | User Guide - Page 253
Displaying a List on the Home Screen To display the elements of a list on the home screen, enter the name of the list (preceded by Ù, if necessary, and then press Í. An ellipsis indicates that the list continues beyond the viewing window. Press ~ repeatedly (or press and hold ~) to scroll the list - Texas Instruments TI 84 | User Guide - Page 254
Resetting memory restores L1 through L6. Removing a list from the stat list editor does not delete it from memory. Using Lists in Graphing You can use lists to graph a family of curves (Chapter 3). Entering List Names Using the LIST NAMES Menu To display the LIST NAMES menu, press y 9. Each item is - Texas Instruments TI 84 | User Guide - Page 255
Note: From the top of a menu, press } to move to the bottom. From the bottom, press † to move to the top. When you select a list name from the LIST NAMES menu, the list name is pasted to the current cursor location. • The list name symbol Ù precedes a list name when the name is pasted where non- - Texas Instruments TI 84 | User Guide - Page 256
must resolve to a list. When anything in the attached formula changes, the list to which the formula is attached is updated automatically. • When you edit an element of a list that is referenced in the formula, the corresponding element in the list to which the formula is attached is updated. • When - Texas Instruments TI 84 | User Guide - Page 257
L4. On the next line, L6!L3(1):L3 changes the first element in L3 to L6, and then redisplays L3. The last screen shows that editing L3 updated ÙADD10, but did not change L4. This is because the formula L3+10 is attached to ÙADD10, but it is not attached to - Texas Instruments TI 84 | User Guide - Page 258
blank line on the home screen or from a program, follow these steps. 1. Press ƒ [ã], enter the you want to attach the formula. • Press y, and then enter a TI-84 Plus list name L1 through L6. • Press y 9 and select a user edit attached formulas, and detach formulas from lists. Chapter 11: Lists 255 - Texas Instruments TI 84 | User Guide - Page 259
a Formula from a List You can detach (clear) an attached formula from a list in several ways. For example: • Enter ã ã !listname on the home screen. • Edit any element of a list to which a formula is attached. • Use the stat list editor (Chapter 12). • Use ClrList or ClrAllList to detach a formula - Texas Instruments TI 84 | User Guide - Page 260
list with a function, the function must be valid for every element in the list. In graphing, an invalid element, such as L1 in ‡({1,0,L1}), is ignored. This returns an error. This graphs X...‡(1) and X...‡(0), but skips X...‡(L1). • When you use two lists with a two-argument function, the dimension - Texas Instruments TI 84 | User Guide - Page 261
• When you use a list and a value with a two-argument function, the value is used with each element in the list. LIST OPS Menu LIST OPS Menu To display the LIST OPS menu, press y 9 ~. NAMES OPS MATH 1: SortA( Sorts lists in ascending order. 2: SortD( Sorts lists in descending order. 3: dim( - Texas Instruments TI 84 | User Guide - Page 262
NAMES OPS MATH 8: Select( Selects specific data points. 9: augment( Concatenates two lists. 0: List4matr( Stores a list to a matrix. A: Matr4list( Stores a matrix to a list. B: Ù Designates the list-name data type. SortA(, SortD( SortA( (sort ascending) sorts list elements from low to high - Texas Instruments TI 84 | User Guide - Page 263
second element of L4, and likewise, 1 becomes the second element of L5. • SortA( and SortD( are the same as SortA( and SortD( on the STAT EDIT menu (Chapter 12). Using dim( to Find List Dimensions dim( (dimension) returns the length (number of elements) of list. dim(list) Chapter 11: Lists 260 - Texas Instruments TI 84 | User Guide - Page 264
Using dim( to Create a List You can use dim( with ¿ to create a new listname with dimension length from 1 to 999. The elements are zeros. length!dim(listname) Using dim( to Redimension a List You can use dim with ¿ to redimension an existing listname to dimension length from 1 to 999. • The elements - Texas Instruments TI 84 | User Guide - Page 265
Fill( Fill( replaces each element in listname with value. Fill(value,listname) Note: dim( and Fill( are the same as dim( and Fill( on the MATRX MATH menu (Chapter 10). seq( seq( (sequence) returns a list in which each element is the result of the evaluation of expression with regard to variable for - Texas Instruments TI 84 | User Guide - Page 266
cumSum( cumSum( (cumulative sum) returns the cumulative sums of the elements in list, starting with the first element. list elements can be real or complex numbers. cumSum(list) @List( @List( returns a list containing the differences between consecutive elements in list. @List subtracts the first - Texas Instruments TI 84 | User Guide - Page 267
example, you can use Select( to select and then analyze a portion of plotted CBL 2™/CBL™ or CBR™ data. Select(xlistname,ylistname) Note: Before you use Select(, you must have selected (turned on) a scatter plot or xyLine plot. Also, the plot must be displayed in the current viewing window. Before - Texas Instruments TI 84 | User Guide - Page 268
2. Enter xlistname, press ¢, enter ylistname, and then press ¤ to designate list names into which you want the selected data to be stored. 3. Press Í. The graph screen is displayed with Left Bound? in the bottom-left corner. 4. Press } or † (if more than one stat plot is selected) to move the - Texas Instruments TI 84 | User Guide - Page 269
7. Press | or ~ to move the cursor to the stat plot point that you want for the right bound, and then press Í. The x-values and y-values of the selected points are stored in xlistname and ylistname. A new stat plot of xlistname and ylistname replaces the stat plot from which you selected data - Texas Instruments TI 84 | User Guide - Page 270
augment( augment( concatenates the elements of listA and listB. The list elements can be real or complex numbers. augment(listA,listB) List4matr( List4matr( (lists stored to matrix) fills matrixname column by column with the elements from each list. If the dimensions of all lists are not equal, then - Texas Instruments TI 84 | User Guide - Page 271
Matr4list( (matrix stored to lists) fills each listname with elements from each column in matrix. If the number of listname arguments exceeds the number of columns in matrix, then Matr4list( ignores extra listname arguments. Likewise, if the number of columns in matrix exceeds the number of listname - Texas Instruments TI 84 | User Guide - Page 272
valid, for example, on the home screen. Without the Ù, the TI-84 Plus may misinterpret a user-created list name as implied multiplication of two or the stat plot editor. If you enter Ù where it is not necessary, the TI-84 Plus will ignore the entry. LIST MATH Menu LIST MATH Menu To display the LIST - Texas Instruments TI 84 | User Guide - Page 273
min(, max( min( (minimum) and max( (maximum) return the smallest or largest element of listA. If two lists are compared, it returns a list of the smaller or larger of each pair of elements in listA and listB. For a complex list, the element with smallest or largest magnitude (modulus) is returned. - Texas Instruments TI 84 | User Guide - Page 274
sum(, prod( sum( (summation) returns the sum of the elements in list. start and end are optional; they specify a range of elements. list elements can be real or complex numbers. prod( returns the product of all elements of list. start and end elements are optional; they specify a range of list - Texas Instruments TI 84 | User Guide - Page 275
stdDev(, variance( stdDev( returns the standard deviation of the elements in list. The default value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. Complex lists are not valid. • variance( returns the variance of the - Texas Instruments TI 84 | User Guide - Page 276
Carolina School of Science and Mathematics, by permission of Janson Publications, Inc., Dedham, MA. 1-800-322-MATH. © 1992. All rights reserved. 1. Press z to set Func graphing mode. Chapter 12: Statistics 273 - Texas Instruments TI 84 | User Guide - Page 277
L1 through L6 in columns 1 through 6. Note: Removing lists from the stat list editor does not delete them from memory. 3. Press ... 1 to select 1:Edit from the STAT EDIT menu. The stat list editor is displayed. If elements are stored in L1 and L2, press } to move the cursor onto L1, and then - Texas Instruments TI 84 | User Guide - Page 278
6. Press o to display the Y= editor. If necessary, press ' to clear the function Y1. As necessary, press }, Í, and ~ to turn off Plot1, Plot2, and Plot3 from the top line of the Y= editor (Chapter 3). As necessary, press †, |, and Í to deselect functions. 7. Press y , 1 to select 1:Plot1 from the - Texas Instruments TI 84 | User Guide - Page 279
. Values for a and b are displayed on the home screen. The linear regression equation is stored in Y1. Residuals are calculated and stored automatically in the list name RESID, which becomes an item on the LIST NAMES menu. 13. Press s. The regression line and the scatter - Texas Instruments TI 84 | User Guide - Page 280
to fit the central portion of the scatter plot well. However, a residual plot may provide more information about this fit. 14. Press ... 1 to select 1:Edit. The stat list editor is displayed. Press ~ and } to move the cursor onto L3. Press y 6. An unnamed column is displayed in column 3; L3, L4 - Texas Instruments TI 84 | User Guide - Page 281
Notice that the first three residuals are negative. They correspond to the shortest pendulum string lengths in L1. The next five residuals are positive, and three of the last four are negative. The latter correspond to the longer string lengths in L1. Plotting the residuals will show this pattern - Texas Instruments TI 84 | User Guide - Page 282
Notice the pattern of the residuals: a group of negative residuals, then a group of positive residuals, and then another group of negative residuals. The residual pattern indicates a curvature associated with this data set for which the linear model did not account. The residual plot emphasizes a - Texas Instruments TI 84 | User Guide - Page 283
the power regression. Values for a and b are displayed on the home screen. The power regression equation is stored in Y1. Residuals are calculated and stored automatically in the list name RESID. 26. Press s. The regression line and the scatter plot are displayed. The new function y=.192x.522 - Texas Instruments TI 84 | User Guide - Page 284
The new residual plot shows that the residuals are random in sign, with the residuals increasing in magnitude as the string length increases. To see the magnitudes of the residuals, continue with these steps. 29. Press r. Press ~ and | to trace the data. Observe the values for Y at each point. With - Texas Instruments TI 84 | User Guide - Page 285
| | | 5 to change the string length to 50 cm. 33. Press Í to calculate the predicted time of about 1.48 seconds. Since a string length of 50 cm exceeds the stored in lists, which you can create and edit using the stat list editor. The TI-84 Plus has six list variables in memory, L1 through - Texas Instruments TI 84 | User Guide - Page 286
details. 1. Enter the statistical data into one or more lists. 2. Plot the data. 3. Calculate the statistical variables or fit a model to the data. 4. Graph the regression equation for the plotted data. 5. Graph the residuals list for the given regression model. Displaying the Stat List Editor The - Texas Instruments TI 84 | User Guide - Page 287
The top line displays list names. L1 through L6 are stored in columns 1 through 6 after a memory reset. The number of the current column is displayed in the top-right corner. The bottom line is the entry line. All data entry occurs on this line. The characteristics of this line change according to - Texas Instruments TI 84 | User Guide - Page 288
2. Enter a valid list name in any of four ways. • Select a name from the LIST NAMES menu (Chapter 11). • Enter L1, L2, L3, L4, L5, or L6 from the keyboard. • Enter an existing user-created list name directly from the keyboard. • Enter a new user-created list name. 3. Press Í or † to store the list - Texas Instruments TI 84 | User Guide - Page 289
To begin entering, scrolling, or editing list elements, press †. The rectangular cursor is displayed. Note: If the list name you entered in step 2 already was stored in another stat list editor - Texas Instruments TI 84 | User Guide - Page 290
Removing a List from the Stat List Editor To remove a list from the stat list editor, move the cursor onto the list name and then press {. The list is not deleted from memory; it is only removed from the stat list editor. Notes: • To delete a list name from memory, use the MEMORY MANAGEMENT/DELETE - Texas Instruments TI 84 | User Guide - Page 291
• On the home screen or in the program editor, enter 0!dim(listname) to set the dimension of listname to 0 (Chapter 11). • Use ClrAllLists to clear all lists in memory (Chapter 18). Editing a List Element To edit a list element, follow these steps. 1. Move the rectangular cursor onto the element you - Texas Instruments TI 84 | User Guide - Page 292
a variable, the stored value is displayed as a list element. When you edit a list element in the stat list editor, the list is updated in memory to a list name in the stat list editor, and then display and edit the calculated list elements. When executed, the attached formula must resolve to a list - Texas Instruments TI 84 | User Guide - Page 293
entry line, then a formula is already attached to the list name. To edit the formula, press Í, and then edit the formula. 4. Press ƒ ããä, enter the formula, and press ƒ ããä. Note: If you do not use quotation marks, the TI-84 Plus calculates and displays the same initial list of answers, but does not - Texas Instruments TI 84 | User Guide - Page 294
is attached (Chapter 11). When a list with a formula attached is displayed in the stat list editor and you edit or enter elements of another displayed list, then the TI-84 Plus takes slightly longer to accept each edit or entry than when no lists with formulas attached are in view. Note: To speed - Texas Instruments TI 84 | User Guide - Page 295
do not want to clear the formula, you can select 1:Quit, display the referenced list on the home screen, and find and edit the source of the error. To edit an element of a list on the home screen, store the new value to listname(element#) (Chapter 11). Detaching Formulas from List Names - Texas Instruments TI 84 | User Guide - Page 296
above, one way to detach a formula from a list name is to edit an element of the list to which the formula is attached. The TI-84 Plus protects against inadvertently detaching the formula from the list name by editing an element of the formula-generated list. Because of the protection feature, you - Texas Instruments TI 84 | User Guide - Page 297
now in view-names context. Press ~ and | to view list names stored in other stat list editor columns. 2. Press Í. You are now in edit-elements context. You may edit any element in a list. All elements of the current list are displayed in braces ( { } )in the entry line. Press ~ and | to view more - Texas Instruments TI 84 | User Guide - Page 298
4. Press Í again. You are now in edit-elements context. You may edit the current element in the entry line. 5. Press } until the cursor is on a list name, then press y 6. You are now in enter-name context. 6. Press '. - Texas Instruments TI 84 | User Guide - Page 299
press ƒ }. To delete a list element, press {. Remaining elements shift up one row. To insert a new element, press y 6. 0 is the default value for a new element. Edit-Elements Context In edit-elements context, the data displayed in the entry line depends on the previous context. • When you switch to - Texas Instruments TI 84 | User Guide - Page 300
all elements in the list are displayed. An ellipsis indicates that list elements continue beyond the screen. You can press ~ and | to edit any element in the list. Note: In edit-elements context, you can attach a formula to a list name only if you switched to it from view-names context. View-Names - Texas Instruments TI 84 | User Guide - Page 301
Enter-Name Context In enter-name context, the Name= prompt is displayed in the entry line, and alpha-lock is on. At the Name= prompt, you can create a new list name, paste a list name from L1 to L6 from the keyboard, or paste an existing list name from the LIST NAMES menu (Chapter 11). The Ù symbol - Texas Instruments TI 84 | User Guide - Page 302
Menu To display the STAT EDIT menu, press .... EDIT CALC TESTS 1: Edit... 2: SortA( 3: SortD( 4: ClrList 5: SetUpEditor Displays the stat list editor. Sorts a list in ascending order. Sorts a list in descending order. Deletes all elements of a list. Stores - Texas Instruments TI 84 | User Guide - Page 303
keylistname. This lets you sort two-variable data on X and keep the data pairs together. All lists must have the same dimension. The sorted lists are updated in memory. SortA(listname) SortD(listname) SortA(keylistname,dependlist1[,dependlist2,...,dependlist n]) SortD(keylistname,dependlist1[, - Texas Instruments TI 84 | User Guide - Page 304
set up the stat list editor to display one or more listnames in the order that you specify. You can specify zero to 20 listnames. Additionally, if you want to use listnames which happen to be archived, the SetUp Editor will automatically unarchive the listnames and place them in the stat - Texas Instruments TI 84 | User Guide - Page 305
Restoring L1 through L6 to the Stat List Editor SetUpEditor with no listnames removes all list names from the stat list editor and restores list names L1 through L6 in the stat list editor columns 1 through 6. Regression Model Features Regression Model Features STAT CALC menu items 3 through C are - Texas Instruments TI 84 | User Guide - Page 306
The TI-84 Plus uses the formula below to compute RESID list elements. The next section describes the whether you specify a Y= variable for regequ, the regression equation always is stored to the TI-84 Plus variable RegEQ, which is item 1 on the VARS Statistics EQ secondary menu. Chapter 12: Statistics - Texas Instruments TI 84 | User Guide - Page 307
to a small number could affect the accuracy of the fit. Diagnostics Display Mode When you execute some regression models, the TI-84 Plus computes and stores diagnostics values for r (correlation coefficient) and r2 (coefficient of determination) or for R2 (coefficient of determination). r and - Texas Instruments TI 84 | User Guide - Page 308
of a regression model when you execute it. However, you can set the diagnostics display mode by executing the DiagnosticOn or DiagnosticOff instruction. Each instruction is in the CATALOG (Chapter 15). Note: To set DiagnosticOn or DiagnosticOff from the home screen, press y N, and then select the - Texas Instruments TI 84 | User Guide - Page 309
... ~. EDIT CALC TESTS 1: 1-Var Stats Calculates 1-variable statistics. 2: 2-Var Stats Calculates 2-variable statistics. 3: Med-Med Calculates a median- . C: SinReg Fits a sinusoidal model to data. D: Manual Linear Fit Fits a linear equation interactively to a scatter plot. Chapter 12 - Texas Instruments TI 84 | User Guide - Page 310
data point or data pair occurs in the data set you are analyzing. For example, if L1={15,12,9,14} and ÙFREQ={1,4,1,3}, then the TI-84 Plus interprets the instruction 1-Var Stats L1, ÙFREQ to mean that 15 occurs once, 12 occurs four times, 9 occurs once, and 14 occurs three times. Each element in - Texas Instruments TI 84 | User Guide - Page 311
,freqlist] Med-Med (ax+b) Med-Med (median-median) fits the model equation y=ax+b to the data using the medianmedian line (resistant line) technique, calculating the summary points x1, y1, x2, y2, x3, and y3. Med-Med displays values for a (slope) and b (y-intercept). Med-Med [Xlistname,Ylistname - Texas Instruments TI 84 | User Guide - Page 312
LinReg(ax+b) [Xlistname,Ylistname,freqlist,regequ] QuadReg (ax2+bx+c) QuadReg (quadratic regression) fits the second-degree polynomial y=ax2+bx+c to the data. It displays values for a, b, and c; when DiagnosticOn is set, it also displays a value for R2. For three data points, the equation is a - Texas Instruments TI 84 | User Guide - Page 313
QuartReg [Xlistname,Ylistname,freqlist,regequ] LinReg-(a+bx) LinReg(a+bx) (linear regression) fits the model equation y=a+bx to the data using a leastsquares fit. It displays values for a (y-intercept) and b (slope); when DiagnosticOn is set, it also displays values for r2 and r. LinReg(a+bx) [ - Texas Instruments TI 84 | User Guide - Page 314
PwrReg (power regression) fits the model equation y=axb to the data using a leastsquares fit and transformed values ln(x) and ln(y). It displays values for a and b; when DiagnosticOn is set, it also displays values for r2 and r. PwrReg [Xlistname,Ylistname,freqlist,regequ] Logistic-c / (1+a...e-bx) - Texas Instruments TI 84 | User Guide - Page 315
order. If you specify period, the algorithm may find a solution more quickly, or it may find a solution when it would not have found one if you had omitted a value for period. If you specify period, the differences between time values in Xlistname can be unequal. Note: The output of SinReg is always - Texas Instruments TI 84 | User Guide - Page 316
one complete period, or cycle. The illustration above and to the right graphically depicts a complete period, or cycle. • Plot the data and trace the previous SinReg execution. Manual Linear Fit Manual Linear Fit allows you to visually fit a linear function to a scatter plot. Manual Linear Fit is an - Texas Instruments TI 84 | User Guide - Page 317
to display the new parameter value. When you edit the value of the selected parameter, the edit can include insert, delete, type over, or displayed graph. The system displays the revised parameter value in the symbolic expression Y=mX+B, and refreshes the graph with the updated Manual-Fit - Texas Instruments TI 84 | User Guide - Page 318
to finish the Manual Fit function. The calculator stores the current mX+b expression into Y1 and makes that function active for graphing. You can also select Manual-Fit while on the Home screen. You can then enter a different Y-Var such as Y4 and then press Í. This takes you to the Graph screen and - Texas Instruments TI 84 | User Guide - Page 319
Variables population standard deviation of y sum of x ... y minimum of x values maximum of x values minimum of y values maximum of y values 1st quartile median 3rd quartile regression/fit coefficients polynomial, Logistic, and SinReg coefficients correlation coefficient coefficient of determination - Texas Instruments TI 84 | User Guide - Page 320
can enter statistical data into lists directly within the program (Chapter 11). Statistical Calculations To perform a statistical calculation from a program, follow these steps. 1. On a blank line in the program editor, select the type of calculation from the STAT CALC menu. 2. Enter the names of - Texas Instruments TI 84 | User Guide - Page 321
or deselect Y= functions as appropriate. 3. Define the stat plot. 4. Turn on the plots you want to display. 5. Define the viewing window. 6. Display and explore the graph. Chapter 12: Statistics 318 - Texas Instruments TI 84 | User Guide - Page 322
Scatter Scatter (")plots plot the data points from Xlist and Ylist as coordinate pairs, showing each point as a box ( › ), cross ( + ), or dot ( ¦ ). Xlist and Ylist must be the same length. You can use the same list for Xlist and Ylist. xyLine xyLine (Ó)is a scatter plot in which the data points - Texas Instruments TI 84 | User Guide - Page 323
Histogram Histogram (Ò) plots one-variable data. The Xscl window variable value determines the width of each bar, beginning at Xmin. ZoomStat adjusts Xmin, Xmax, Ymin, and Ymax to include all values, and also adjusts Xscl. The inequality (Xmax N Xmin) à Xscl 47 must be true. A value that occurs on - Texas Instruments TI 84 | User Guide - Page 324
in the middle. When three are plotted, the first one plots at the top, the second in the middle, and the third at the bottom. Boxplot Boxplot (Ö)(regular box plot) plots one-variable data. The whiskers on the plot extend from the minimum data point in the set (minX) to the first quartile (Q1) and - Texas Instruments TI 84 | User Guide - Page 325
name in the Data List field. Select X or Y for the Data Axis setting. • If you select X, the TI-84 Plus plots the data on the x-axis and the z-values on the y-axis. • If you select Y, the TI-84 Plus plots the data on the y-axis and the z-values on the x-axis. Defining the Plots To define - Texas Instruments TI 84 | User Guide - Page 326
1. Press y ,. The STAT PLOTS menu is displayed with the current plot definitions. 2. Select the plot you want to use. The stat plot editor is displayed for the plot you selected. 3. Press Í to select On if you want to plot the statistical data immediately. The definition is stored whether you - Texas Instruments TI 84 | User Guide - Page 327
Plot Type Õ ModBoxplot Ö Boxplot Ô NormProbPlot XList YList œ œ œ Mark Freq Data List œ œ _ Data Axis œ œ _ 5. Enter list names or select options for the plot type. • Xlist (list name containing independent data) • Ylist (list name containing dependent data) • Mark (› or + or ¦) • - Texas Instruments TI 84 | User Guide - Page 328
Turning On and Turning Off Stat Plots PlotsOn and PlotsOff allow you to turn on or turn off stat plots from the home screen or a program. With no plot number, PlotsOn turns on all plots and PlotsOff turns off all plots. With one or more plot numbers (1, 2, and 3), PlotsOn turns on - Texas Instruments TI 84 | User Guide - Page 329
(Chapter 3). When ExprOn is selected, the plot number and plotted data lists are displayed in the top-left corner. Statistical Plotting in a Program Defining a Stat Plot in a Program To display a stat plot from a program, define the plot, and then display the graph. Chapter 12: Statistics 326 - Texas Instruments TI 84 | User Guide - Page 330
To define a stat plot from a program, begin on a blank line in the program editor and enter data into one or more lists; then, follow these steps. 1. Press y , to display the STAT PLOTS menu. 2. Select the plot to define, - Texas Instruments TI 84 | User Guide - Page 331
point. The selected mark symbol is pasted to the cursor location. 7. Press ¤ Í to complete the command line. Displaying a Stat Plot from a Program To display a plot from a program, use the DispGraph instruction (Chapter 16) or any of the ZOOM instructions (Chapter 3). Chapter 12: Statistics 328 - Texas Instruments TI 84 | User Guide - Page 332
Chapter 12: Statistics 329 - Texas Instruments TI 84 | User Guide - Page 333
Chapter 13: Inferential Statistics and Distributions Getting Started: Mean Height of a Population Getting Started is a fast-paced introduction. Read the chapter for details. Suppose you want to estimate the mean height of a population of women given the random sample below. Because heights among a - Texas Instruments TI 84 | User Guide - Page 334
2. Enter [H] [G] [H] [T] at the Name= prompt, and then press Í. The list to which you will store the women's height data is created. Press † to move the cursor onto the first row of the list. HGHT(1)= is displayed on the bottom line. 3. Press 169 Ë 43 to enter the first height value. As you enter it - Texas Instruments TI 84 | User Guide - Page 335
large number of samples, we expect 99 percent of the intervals calculated to contain the population mean. The actual mean of the population sampled is 165.1 centimeters, which is in the calculated interval. The second line gives the mean height of the sample v - Texas Instruments TI 84 | User Guide - Page 336
to store 163.8 to v. Press 7 Ë 1 Í to store 7.1 to Sx. Press 90 Í to store 90 to n. 9. Press † to move the cursor onto Calculate, and then press Í to calculate the new 99 percent confidence interval. The results are displayed on the home screen. Chapter 13: Inferential Statistics and Distributions - Texas Instruments TI 84 | User Guide - Page 337
m, and 6.35 is s. The result is displayed on the home screen; it shows that five percent of the women are taller than 175.5 centimeters. Now graph and shade the top 5 percent of the population. 12. Press p and set the window variables to these values. Xmin=145 Ymin=L.02 Xmax=185 Ymax - Texas Instruments TI 84 | User Guide - Page 338
. up is the upper bound. Inferential Stat Editors Displaying the Inferential Stat Editors When you select a hypothesis test or confidence interval instruction from the home screen, the appropriate inferential statistics editor is displayed. The editors vary Chapter 13: Inferential Statistics and - Texas Instruments TI 84 | User Guide - Page 339
inferential stat editor for T-Test. Note: When you select the ANOVA( instruction, it is pasted to the home screen. ANOVA( does not have selection is available. 6. Select Calculate or Draw (when Draw is available) to execute the instruction. • When you select Calculate, the results are displayed on - Texas Instruments TI 84 | User Guide - Page 340
describes the selections in the above steps for each hypothesis test and confidence interval instruction. Select Data or Stats input Enter values for arguments Select an alternative hypothesis Select Calculate or Draw output Selecting Data or Stats Most inferential stat editors prompt you to - Texas Instruments TI 84 | User Guide - Page 341
you enter values in any inferential stat editor, the TI-84 Plus stores them in memory so that you can run many (2-SampTTest and 2-SampTInt only) specifies whether the variances are to be pooled for the calculation. • Select No if you do not want the variances pooled. Population variances can be - Texas Instruments TI 84 | User Guide - Page 342
The window variables are adjusted automatically to fit the graph. To select Calculate or Draw, move the cursor to either Calculate or Draw, and then press Í. The instruction is immediately executed. Selecting Calculate for a Confidence Interval After you have entered all arguments in an inferential - Texas Instruments TI 84 | User Guide - Page 343
hypothesis test or confidence interval instruction to a command line in a program. From within the program editor, select the instruction from either the CATALOG instructions store some output variables to memory. For a list of these variables, see the Test and Interval Output Variables table. EDIT - Texas Instruments TI 84 | User Guide - Page 344
EDIT CALC TESTS 0: 2-SampTInt... A: 1-PropZInt... B: 2-PropZInt... C: c2-Test... D: c2-GOF Test... E: 2- Instructions In this chapter, the description of each STAT TESTS instruction shows the unique inferential stat editor for that instruction with example arguments. • Descriptions of instructions - Texas Instruments TI 84 | User Guide - Page 345
with the example results. • Descriptions of instructions that offer the Calculate/Draw output choice show both types of screens: calculated and graphic results. • Descriptions of instructions that offer only the Calculate output choice show the calculated results on the home screen. Z-Test - Texas Instruments TI 84 | User Guide - Page 346
L1={299.4 297.7 301 298.9 300.2 297} Data Input: Stats Calculated results: Drawn results: Chapter 13: Inferential Statistics and Distributions 343 - Texas Instruments TI 84 | User Guide - Page 347
Note: All STAT TESTS examples assume a fixed-decimal mode setting of 4 (Chapter 1). If you set the decimal mode to Float or a different fixed-decimal setting, your output may differ from the output in the examples. T-Test T-Test (one-sample t test; item 2) performs a hypothesis test for a single - Texas Instruments TI 84 | User Guide - Page 348
Data Calculated results: Stats Drawn results: 2-SampZTest 2-SampZTest (two-sample z test; item 3) tests the equality of the means of two populations (m1 and m2) based on independent - Texas Instruments TI 84 | User Guide - Page 349
In the example: LISTA={154 109 137 115 140} LISTB={108 115 126 92 146} Data Input: Stats Calculated results: Chapter 13: Inferential Statistics and Distributions 346 - Texas Instruments TI 84 | User Guide - Page 350
Data Drawn results: Stats 2-SampTTest 2-SampTTest (two-sample t test; item 4) tests the equality of the means of two populations (m1 and m2) based on independent samples when neither population standard deviation (s1 or s2) is known. The null hypothesis H0: m1=m2 is tested against one of the - Texas Instruments TI 84 | User Guide - Page 351
SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.642} Data Input: Stats Calculated results: Chapter 13: Inferential Statistics and Distributions 348 - Texas Instruments TI 84 | User Guide - Page 352
Data Drawn results: Stats 1-PropZTest 1-PropZTest (one-proportion z test; item 5) computes a test for an unknown proportion of successes (prop). It takes as input the count of successes in the sample x and the count of observations in the sample n. 1-PropZTest tests the null hypothesis H0: prop=p0 - Texas Instruments TI 84 | User Guide - Page 353
Calculated results: Drawn results: 2-PropZTest 2-PropZTest (two-proportion z test; item 6) computes a test to compare the proportion of successes (p1 and p2) from two populations. It takes - Texas Instruments TI 84 | User Guide - Page 354
• Ha: p1>p2 (p1:>p2) Input: Calculated results: Drawn results: Chapter 13: Inferential Statistics and Distributions 351 - Texas Instruments TI 84 | User Guide - Page 355
known. The computed confidence interval depends on the user-specified confidence level. In the example: L1={299.4 297.7 301 298.9 300.2 297} Data Input: Stats Calculated results: Chapter 13: Inferential Statistics and Distributions 352 - Texas Instruments TI 84 | User Guide - Page 356
m when the population standard deviation s is unknown. The computed confidence interval depends on the user-specified confidence level. In the example: L6={1.6 1.7 1.8 1.9} Data Input: Stats Calculated results: Chapter 13: Inferential Statistics and Distributions 353 - Texas Instruments TI 84 | User Guide - Page 357
2-SampZInt 2-SampZInt (two-sample z confidence interval; item 9) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are known. The computed confidence interval depends on the user-specified confidence level. In - Texas Instruments TI 84 | User Guide - Page 358
Data Calculated results: Stats 2-SampTInt 2-SampTInt (two-sample t confidence interval; item 0) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations ( - Texas Instruments TI 84 | User Guide - Page 359
SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.642} Data Input: Stats Calculated results: Chapter 13: Inferential Statistics and Distributions 356 - Texas Instruments TI 84 | User Guide - Page 360
the count of observations in the sample n. The computed confidence interval depends on the user-specified confidence level. Input: Calculated results: 2-PropZInt 2-PropZInt (two-proportion z confidence interval; item B) computes a confidence interval for the difference between the proportion of - Texas Instruments TI 84 | User Guide - Page 361
observations in each sample (n1 and n2). The computed confidence interval depends on the user-specified confidence level. Input: Calculated results: c2-Test c2-Test (chi-square test; item C) computes a chi-square test for association on the twoway table of counts in the specified Observed - Texas Instruments TI 84 | User Guide - Page 362
variable name to which you want the computed expected counts to be stored; default=[B]. Matrix editor: Note: Press y ú ~ ~ 1 to select 1:[A] from the MATRX EDIT menu. Input: Calculated results: Note: Press y to display matrix [B]. Chapter 13: Inferential Statistics and Distributions 359 - Texas Instruments TI 84 | User Guide - Page 363
Drawn results: c2GOF-Test c2GOF-Test (Chi Square Goodness of Fit; item D) performs a test to confirm that sample data is from a population that conforms to a specified distribution. For example, c2 GOF can confirm that the sample data came from a normal distribution. In the example: list 1={16,25, - Texas Instruments TI 84 | User Guide - Page 364
Calculated results: Drawn results: 2-SampFTest 2-SampÜTest (two-sample Ü-test; item E) computes an Ü-test to compare two normal population standard deviations (s1 and s2). The population - Texas Instruments TI 84 | User Guide - Page 365
In the example: SAMP4={ SAMP5={ 7 L4 18 17 L3 L5 1 10 11 L2} L1 12 L1 L3 3 L5 5 2 L11 L1 L3} Data Input: Stats Calculated results: Chapter 13: Inferential Statistics and Distributions 362 - Texas Instruments TI 84 | User Guide - Page 366
EQ secondary menu). If you enter a Y= variable name at the RegEQ: prompt, the calculated regression equation is automatically stored to the specified Y= equation. In the example below, the regression ={ L4={ 38 56 59 64 74} 41 63 70 72 84} Chapter 13: Inferential Statistics and Distributions 363 - Texas Instruments TI 84 | User Guide - Page 367
Input: Calculated results: When LinRegTTest is executed, the list of residuals is created and stored to the list name RESID automatically. RESID is placed on the LIST - Texas Instruments TI 84 | User Guide - Page 368
1={4, 5, 6, 7, 8} list 2={1, 2, 3, 3.5, 4.5} LinRegTInt input screen: Note: Press ... ~ ~ to select TESTS. Press † several times to select G:LinRegTint... Press Í. Press † several times to select Calculate. Press Í. Calculated results: Chapter 13: Inferential Statistics and Distributions 365 - Texas Instruments TI 84 | User Guide - Page 369
Xlist, Ylist is the list of independent and dependent variables. The list containing the Freq (frequency) values for the data is stored in List. The default is 1. All elements must be real numbers. Each element in the Freq list is the frequency of occurence for each corresponding data point in the - Texas Instruments TI 84 | User Guide - Page 370
Calculated results: Note: SS is sum of squares and MS is mean square. Inferential Statistics Input Descriptions The tables in this section describe the inferential statistics - Texas Instruments TI 84 | User Guide - Page 371
output to generate for tests and intervals. Calculate displays the output on the home screen. In tests, Draw draws a graph of the results. v, Sx, n Summary 2-SampTTest and 2-SampTInt. No instructs the TI-84 Plus not to pool the variances. Yes instructs the TI-84 Plus to pool the variances. Chapter - Texas Instruments TI 84 | User Guide - Page 372
be an integer > 0. The count of observations in sample two for the 2-PropZTest and 2-PropZInt. Must be an integer > 0. The confidence level for the interval instructions. Must be , 0 and < 100. If it is , 1, it is assumed to be given as a percent and is divided by 100. Default=0.95. The matrix name - Texas Instruments TI 84 | User Guide - Page 373
L1 and L2, respectively. The dimensions of Xlist and Ylist must be the same. The prompt for the name of the Y= variable where the calculated regression equation is to be stored. If a Y= variable is specified, that equation is automatically selected (turned on). The default is to store the regression - Texas Instruments TI 84 | User Guide - Page 374
Variables number of data points for sample 1 and sample 2 pooled standard deviation estimated sample proportion estimated sample proportion for population 1 estimated sample proportion for population 2 confidence interval pair mean of x values sample standard deviation of x number of data points - Texas Instruments TI 84 | User Guide - Page 375
Distribution Functions DISTR menu To display the DISTR menu, press y =. DISTR DRAW 1: normalpdf( 2: normalcdf( 3: invNorm( 4: invT( 5: tpdf( 6: tcdf( 7: c2pdf( 8: c2cdf 9: Üpdf( 0: Ücdf( A: binompdf( nn probability density function nn cumulative distribution function Inverse cumulative normal - Texas Instruments TI 84 | User Guide - Page 376
DISTR DRAW B: binomcdf( C: poissonpdf( D: poissoncdf( E: geometpdf( F: geometcdf( Binomial cumulative density Poisson probability Poisson cumulative density Geometric probability Geometric cumulative density Note: L1â99 and 1â99 specify infinity. If you want to view the area left of upperbound, - Texas Instruments TI 84 | User Guide - Page 377
normalpdf(x[,m,s]) Note: For this example, Xmin = 28 Xmax = 42 Ymin = 0 Ymax = .2 Xscl = 1 Yscl = .1 Note: For plotting the normal distribution, you can set window variables Xmin and Xmax so that the mean m falls between them, and then select 0:ZoomFit from the ZOOM menu. normalcdf( normalcdf( - Texas Instruments TI 84 | User Guide - Page 378
the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by mean m and standard deviation s. It calculates the x value associated with an area to the left of the x value. 0 area 1 must be true. The defaults are m=0 and s=1. invNorm - Texas Instruments TI 84 | User Guide - Page 379
tpdf( tpdf( computes the probability density function (pdf) for the Student-t distribution at a specified x value. df (degrees of freedom) must be > 0. To plot the Student-t distribution, paste tpdf( to the Y= editor. The probability density function (pdf) is: f(x d----f---+-----1---)---/-2----] - Texas Instruments TI 84 | User Guide - Page 380
c2pdf( c2pdf( computes the probability density function (pdf) for the c2 (chi-square) distribution at a specified x value. df (degrees of freedom) must be an integer > 0. To plot the c2 distribution, paste c2pdf( to the Y= editor. The probability density function (pdf) is: f(x - Texas Instruments TI 84 | User Guide - Page 381
c2cdf( c2cdf( computes the c2 (chi-square) distribution probability between lowerbound and upperbound for the specified df (degrees of freedom), which must be an integer > 0. c2cdf(lowerbound,upperbound,df) Fpdf( Üpdf( computes the probability density function (pdf) for the Ü distribution at a - Texas Instruments TI 84 | User Guide - Page 382
Üpdf(x,numerator df,denominator df) Note: For this example, Xmin = 0 Xmax = 5 Ymin = 0 Ymax = 1 Fcdf( Ücdf( computes the Ü distribution probability between lowerbound and upperbound for the specified numerator df (degrees of freedom) and denominator df. numerator df and denominator df must be - Texas Instruments TI 84 | User Guide - Page 383
of integers. 0p1 must be true. numtrials must be an integer > 0. If you do not specify x, a list of probabilities from 0 to numtrials is returned. The probability density function (pdf) is: f(x) = ⎛ ⎝ n⎞ x⎠ px(1 - p )n - x,x = 0,1,...,n where n = numtrials binompdf(numtrials,p[,x]) - Texas Instruments TI 84 | User Guide - Page 384
poissonpdf( poissonpdf( computes a probability at x for the discrete Poisson distribution with the specified mean m, which must be a real number > 0. x can be an integer or a list of integers. The probability density function (pdf) is: f(x) = e-µµx ⁄ x!,x = 0,1,2,... poissonpdf(m,x) poissoncdf( - Texas Instruments TI 84 | User Guide - Page 385
number or a list of real numbers. geometcdf(p,x) Distribution Shading DISTR DRAW Menu To display the DISTR DRAW menu, press y = ~. DISTR DRAW instructions draw various types of density functions, shade the area specified by lowerbound and upperbound, and display the computed area value. Chapter - Texas Instruments TI 84 | User Guide - Page 386
To clear the drawings, select 1:ClrDraw from the DRAW menu (Chapter 8). Note: Before you execute a DISTR DRAW instruction, you must set the window variables so that the desired distribution fits the screen. DISTR DRAW 1: ShadeNorm( 2: Shade_t( 3: Shadec2( 4: ShadeÜ( Shades normal distribution. - Texas Instruments TI 84 | User Guide - Page 387
ShadeNorm(lowerbound,upperbound[,m,s]) Note: For this example, Xmin = 55 Xmax = 72 Ymin = L.05 Ymax = .2 Shade_t( Shade_t( draws the density function for the Student-t distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound. Shade_t(lowerbound, - Texas Instruments TI 84 | User Guide - Page 388
Shadec2( Shadec2( draws the density function for the c2 (chi-square) distribution specified by df (degrees of freedom) and shades the area between lowerbound and upperbound. Shadec2(lowerbound,upperbound,df) Note: For this example, Xmin = 0 Xmax = 35 Ymin = L.025 Ymax = .1 ShadeF( ShadeÜ( draws the - Texas Instruments TI 84 | User Guide - Page 389
ShadeÜ(lowerbound,upperbound,numerator df,denominator df) Note: For this example, Xmin = 0 Xmax = 5 Ymin = L.25 Ymax = .9 Chapter 13: Inferential Statistics and Distributions 386 - Texas Instruments TI 84 | User Guide - Page 390
for applications. Your TI-84 Plus includes Flash applications in addition to the ones mentioned above. Press ŒÎ to see the complete list of applications that came with your calculator. Documentation for applications are on the Texas Instruments Web site at: education.ti.com/guides . Steps for - Texas Instruments TI 84 | User Guide - Page 391
a car you would like to buy. The car costs 9,000. You can afford payments of 250 per month for four years. What annual percentage rate (APR) will make it possible for you to afford the car? 1. Press z to set the fixed-decimal mode setting to 2. The TI-84 Plus will display all numbers with - Texas Instruments TI 84 | User Guide - Page 392
the CALC VARS menu. The TVM Solver is displayed. Press 48 Í to store 48 months to Ú. Press † 9000 Í to store 9,000 to PV. Press Ì 250 Í to store L250 to PMT. (Negation indicates - Texas Instruments TI 84 | User Guide - Page 393
there are no payments when you solve compound interest problems, PMT must be set to 0 and P/Y must be set to 1. 1. Press Œ Í to select 1:Finance from the APPLICATIONS menu. 2. Press Í to select 1:TVM Solver from the CALC VARS menu. The TVM Solver is displayed. Press 7 to enter the number of periods - Texas Instruments TI 84 | User Guide - Page 394
period) and Pmt_Bgn (payment at the beginning of each period). To solve for an unknown TVM variable, follow these steps. 1. Press Œ Í Í to display the TVM Solver. The screen below shows the default values with the fixed-decimal mode set to two decimal places. 2. Enter the known values for four TVM - Texas Instruments TI 84 | User Guide - Page 395
is computed, displayed in the TVM Solver, and stored to the appropriate TVM variable. An indicator square in the left column designates the solution variable. Using the Financial Functions Entering Cash Inflows and Cash Outflows When using the TI-84 Plus financial functions, you must enter cash - Texas Instruments TI 84 | User Guide - Page 396
the FINANCE CALC menu, press ÎŒ Í. CALC VARS 1: TVM Solver... Displays the TVM Solver. 2: tvm_Pmt Computes the amount of each payment. 3: tvm_¾æ rate. C: 4Eff( Computes the effective interest rate. D: dbd( Calculates the days between two dates. E: Pmt_End Selects ordinary annuity (end - Texas Instruments TI 84 | User Guide - Page 397
to the TVM variables. Note: To store a value to a TVM variable, use the TVM Solver or use ¿ and any TVM variable on the FINANCE VARS menu. If you enter less than six arguments, the TI-84 Plus substitutes a previously stored TVM variable value for each unspecified argument. If you enter any arguments - Texas Instruments TI 84 | User Guide - Page 398
,FV,P/Y,C/Y)] Note: In the example above, the values are stored to the TVM variables in the TVM Solver. Then the payment (tvm_Pmt) is computed on the home screen using the values in the TVM Solver. Next, the interest rate is changed to 9.5 to illustrate the effect on the payment amount. tvm_I% tvm_ - Texas Instruments TI 84 | User Guide - Page 399
tvm_PV[(Ú,¾æ,PMT,FV,P/Y,C/Y)] tvm_N tvm_Ú computes the number of payment periods. tvm_Ú[(æ¾,PV,PMT,FV,P/Y,C/Y)] tvm_FV tvm_FV computes the future value. tvm_FV[(Ú,¾æ,PV,PMT,P/Y,C/Y)] Chapter 14: Applications 396 - Texas Instruments TI 84 | User Guide - Page 400
Cash Flows Calculating a Cash Flow Use the cash flow functions (menu items 7 and 8) to analyze the value of money over equal time periods. You can enter unequal cash - Texas Instruments TI 84 | User Guide - Page 401
npv(, irr( npv( (net present value) is the sum of the present values for the cash inflows and outflows. A positive result for npv indicates a profitable investment. npv(interest rate,CF0,CFList[,CFFreq]) irr( (internal rate of return) is the interest rate at which the net present value of the cash - Texas Instruments TI 84 | User Guide - Page 402
a balance. It must be a positive integer < 10,000. roundvalue specifies the internal precision the calculator uses to calculate the balance; if you do not specify roundvalue, then the TI-84 Plus uses the current Float/Fix decimal-mode setting. bal(npmt[,roundvalue]) GPrn(, GInt( GPrn( computes the - Texas Instruments TI 84 | User Guide - Page 403
the interest; if you do not specify roundvalue, the TI-84 Plus uses the current Float/Fix decimal-mode setting. GInt(pmt1,pmt2[,roundvalue]) Amortization Example: Calculating an Outstanding Loan Balance You want to buy a home with a 30-year mortgage at 8 percent APR. Monthly payments are 800 - Texas Instruments TI 84 | User Guide - Page 404
2. Press to display the TVM Solver. 3. Press 360 to enter number of payments. Press † 8 to enter =50 Ymin=0 Ymax=125000 Yscl=10000 7. Press r to draw the graph and activate the trace cursor. Press ~ and | to explore the graph of the outstanding balance over time. Press a number and then press - Texas Instruments TI 84 | User Guide - Page 405
(Y1T). 10. Press z to select G-T split-screen mode, in which the graph and table are displayed simultaneously. Press r to display X1T (time) and Y1T (balance) in the table. Calculating Interest Conversion Calculating an Interest Conversion Use the interest conversion functions (menu items B and - Texas Instruments TI 84 | User Guide - Page 406
periods must be >0. 4Eff(nominal rate,compounding periods) Finding Days between Dates/Defining Payment Method dbd( Use the date function dbd( (menu item D) to calculate the number of days between two dates using the actual-day-count method. date1 and date2 can be numbers or lists of numbers within - Texas Instruments TI 84 | User Guide - Page 407
Pmt_End and Pmt_Bgn (menu items E and F) specify a transaction as an ordinary annuity or an annuity due. When you execute either command, the TVM Solver is updated. Pmt_End Pmt_End (payment end) specifies an ordinary annuity, where payments occur at the end of each payment period. Most loans are in - Texas Instruments TI 84 | User Guide - Page 408
beginning) specifies an annuity due, where payments occur at the beginning of each payment period. Most leases are in this category. Pmt_Bgn On the TVM Solver's PMT:END BEGIN line, select BEGIN to set PMT to annuity due. Using the TVM Variables FINANCE VARS Menu To display the FINANCE VARS menu - Texas Instruments TI 84 | User Guide - Page 409
you have stored a value to P/Y. The EasyData App The EasyData App by Vernier Software and Technology allows you to view and analyze real-world data when the TI-84 Plus is connected to data collection devices such as Texas Instruments CBR 2é, CBL 2é, Vernier LabProê, Vernier USB sensors, Vernier - Texas Instruments TI 84 | User Guide - Page 410
. Starting EasyData 1. Attach your data collection device to your TI-84 Plus. Make sure the cables are firmly connected. 2. If the EasyData app has not auto-launched, press Œ and the } or † to select the EasyData App. 3. Press Í. The EasyData information screen is displayed for about three seconds - Texas Instruments TI 84 | User Guide - Page 411
setting: 1. From the main screen in the EasyData App, choose Setup and select 2: Time Graph. The current settings are displayed on the calculator. Note: If using a motion detector, settings collection device is connected to the TI-84 Plus, choose File and select 1:New. Chapter 14: Applications 408 - Texas Instruments TI 84 | User Guide - Page 412
to the TI-84 Plus and stored in lists L1 through L4 when data collection is complete. When you exit the EasyData App, a prompt reminds you of the lists in which time, distance, velocity, and acceleration are stored. For more information about the EasyData app, refer to the Texas Instrument Web site - Texas Instruments TI 84 | User Guide - Page 413
Chapter 14: Applications 410 - Texas Instruments TI 84 | User Guide - Page 414
alphabetical list of all functions and instructions on the TI-84 Plus. You also can access each CATALOG item from a menu or the keyboard, except: • The six string functions • The six hyperbolic functions • The solve( instruction without the equation solver editor (Chapter 2) • The inferential stat - Texas Instruments TI 84 | User Guide - Page 415
The 4 in the first column is the selection cursor. 2. Press † or } to scroll the CATALOG until the selection cursor points to the item you want. • To jump to the first item beginning with a particular letter, press that letter; alpha- lock is on. • Items that begin with a number are in alphabetical - Texas Instruments TI 84 | User Guide - Page 416
or function name, such as sin( or cos(, as one character; the TI-84 Plus interprets each instruction or function name as one character. Entering a String To enter a string on a blank line on the home screen or in a program, follow these steps. 1. Press ƒ [ã] to indicate the beginning of the string - Texas Instruments TI 84 | User Guide - Page 417
do not count as string characters. Storing Strings to String Variables String Variables The TI-84 Plus has 10 variables to which you can store strings. You can use string variables with string functions and instructions. To display the VARS STRING menu, follow these steps. 1. Press to display the - Texas Instruments TI 84 | User Guide - Page 418
2. Press Í to display the STRING secondary menu. Storing a String to a String Variable To store a string to a string variable, follow these steps. 1. Press ƒ [ã], enter the string, and press ƒ [ã]. 2. Press ¿. 3. Press 7 to display the VARS STRING menu. 4. Select the string variable (from Str1 to - Texas Instruments TI 84 | User Guide - Page 419
from the VARS STRING menu, and then press Í. The string is displayed. String Functions and Instructions in the CATALOG Displaying String Functions and Instructions in the CATALOG String functions and instructions are available only from the CATALOG. The table below lists the string functions and - Texas Instruments TI 84 | User Guide - Page 420
other CATALOG menu items. The ellipses in the table indicate the presence of additional CATALOG items. CATALOG ... Equ4String( expr( ... inString( ... length( ... String4Equ( sub( ... Converts an equation to a string. Converts a string to an expression. Returns a character's place number. Returns - Texas Instruments TI 84 | User Guide - Page 421
+string2+string3... 4. Press Í to display the strings as a single string. Selecting a String Function from the CATALOG To select a string function or instruction and paste it to the current screen, follow the steps for selecting an item from the CATALOG. Equ4String( Equ4String( converts to a string - Texas Instruments TI 84 | User Guide - Page 422
expr( expr( converts the character string contained in string to an expression and executes it. string can be a string or a string variable. expr(string) inString( inString( returns the character position in string of the first character of substring. string can be a string or a string variable. - Texas Instruments TI 84 | User Guide - Page 423
length( length( returns the number of characters in string. string can be a string or string variable. Note: An instruction or function name, such as sin( or cos(, counts as one character. length(string) String4Equ( String4Equ( converts string into an equation and stores the equation - Texas Instruments TI 84 | User Guide - Page 424
of the subset. length is the number of characters in the subset. sub(string,begin,length) Entering a Function to Graph during Program Execution In a program, you can enter a function to graph during program execution using these commands. Chapter 15: CATALOG, Strings, Hyperbolic Functions 421 - Texas Instruments TI 84 | User Guide - Page 425
Note: When you execute this program, enter a function to store to Y3 at the ENTRY= prompt. among the other CATALOG menu items. The ellipses in the table indicate the presence of additional CATALOG items. CATALOG ... cosh( cosh-1( ... sinh( Hyperbolic cosine Hyperbolic arccosine Hyperbolic sine - Texas Instruments TI 84 | User Guide - Page 426
CATALOG sinh-1( ... tanh( tanh-1( ... Hyperbolic arcsine Hyperbolic tangent Hyperbolic arctangent sinh(, cosh(, tanh( sinh(, cosh(, and tanh( are the hyperbolic functions. Each is valid for real numbers, expressions, and lists. sinh(value) cosh(value) tanh(value) sinh-1(, cosh-1(, tanh-1( sinh-1( - Texas Instruments TI 84 | User Guide - Page 427
sinh-1(value) cosh-1(value) sinh-1(value) Chapter 15: CATALOG, Strings, Hyperbolic Functions 424 - Texas Instruments TI 84 | User Guide - Page 428
Cylinder Getting Started is a fast-paced introduction. Read the chapter for details. A program is a set of commands that the TI-84 Plus executes sequentially, as if you had entered them from the keyboard. Create a program that prompts for the radius R and the height H of a cylinder and then computes - Texas Instruments TI 84 | User Guide - Page 429
from the PRGM I/O menu. Disp is pasted to the command line. Press y 7 [ã] [V] [O] [L] [U] [M] [E] O [I] [S V] Í to set up the program to display the text VOLUME IS on one line and the calculated value of V on the next. 6. Press y 5 to display the home screen. 7. Press to display the PRGM EXEC - Texas Instruments TI 84 | User Guide - Page 430
or more command lines. Each line contains one or more instructions. When you execute a program, the TI-84 Plus performs each instruction on each command line in the same order in which you entered them. The number and size of programs that the TI-84 Plus can store is limited only by available memory - Texas Instruments TI 84 | User Guide - Page 431
. The Name= prompt is displayed, and alpha-lock is on. 3. Press a letter from A to Z or q to enter the first character of the new program name. Note: A program name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be - Texas Instruments TI 84 | User Guide - Page 432
The TI-84 Plus expresses memory quantities in bytes. You can increase available memory in one of two ways. You can delete one or more programs or you can archive some programs. To increase available memory by deleting a specific program: 1. Press y L and then select 2:Mem Mgmt/Del from the MEMORY - Texas Instruments TI 84 | User Guide - Page 433
will disappear. Note: Archive programs cannot be edited or executed. In order to edit or execute an archived program, you must first unarchive it. Entering Command Lines and Executing Programs Entering a Program Command Line You can enter on a command line any instruction or expression that you - Texas Instruments TI 84 | User Guide - Page 434
menu. prgmname is pasted to the home screen (for example, prgmCYLINDER). 3. Press Í to execute the program. While the program is executing, the busy indicator is on. Last Answer (Ans) is updated during program execution. Last Entry is not updated as each command is executed (Chapter 1). Chapter 16 - Texas Instruments TI 84 | User Guide - Page 435
The TI-84 Plus checks for errors during program execution. It does not check for errors as you enter a program. Breaking a Program To stop program execution, press É. The ERR:BREAK menu is displayed. • To return to the home screen, select 1:Quit. • To go where the interruption occurred, select 2: - Texas Instruments TI 84 | User Guide - Page 436
the line, press ' to clear all instructions and expressions on the line, and then press { to delete the command line, including the colon. Copying and Renaming Programs Copying and Renaming a Program To copy all command lines from one program into a new program, follow steps 1 through 5 for Creating - Texas Instruments TI 84 | User Guide - Page 437
groups of instructions that you use frequently. • You can rename a program by copying its contents into a new program. Note: You also can copy all the command lines from one existing program to another existing program using RCL. Scrolling the PRGM EXEC and PRGM EDIT Menus The TI-84 Plus sorts PRGM - Texas Instruments TI 84 | User Guide - Page 438
PRGM CTL (Control) Instructions PRGM CTL Menu To display the PRGM CTL (program control) menu, press from the program editor only. CTL I/O EXEC 1: If 2: Then 3: Else 4: For( 5: While 6: Repeat 7: End 8: Pause 9: Lbl 0: Goto A: IS>( B: DS - Texas Instruments TI 84 | User Guide - Page 439
to the cursor location on a command line in the program. To return to the program editor without selecting an item, press '. Controlling Program Flow Program control instructions tell the TI-84 Plus which command to execute next in a program. If, While, and Repeat check a defined condition to - Texas Instruments TI 84 | User Guide - Page 440
command immediately following If is skipped. If condition is true (nonzero), then the next command is executed. If instructions can be nested. :If condition :command (if true) :command Program Output If-Then Then following an If executes a group of commands if condition is true (nonzero). End - Texas Instruments TI 84 | User Guide - Page 441
the end of the group of commands. :If condition :Then :command (if true) :command (if true) :Else :command (if false) :command (if false) :End :command Program Output Chapter 16 - Texas Instruments TI 84 | User Guide - Page 442
of the loop. For( loops can be nested. :For(variable,begin,end[,increment]) :command (while end not exceeded) :command (while end not exceeded) :End :command Program Output Chapter 16 - Texas Instruments TI 84 | User Guide - Page 443
when While is encountered. If condition is true (nonzero), the program executes a group of commands. End signifies the end of the group. When condition is false (zero), the program executes each command following End. While instructions can be nested. :While condition :command (while condition is - Texas Instruments TI 84 | User Guide - Page 444
For(, While, or Repeat loop. Also, you must paste an End instruction at the end of each If-Then group and each If-Then-Else group. Pause Pause suspends execution of the program so that you can see answers or graphs. During the pause, the pause indicator is on in the top-right - Texas Instruments TI 84 | User Guide - Page 445
Pause [value] Program Output Lbl, Goto Lbl (label) and Goto (go to) are used together for branching. Lbl specifies the label for a command. label can be one or two characters (A through Z, 0 through 99, or q). Lbl label Goto causes the program to branch to label when Goto is encountered. Chapter - Texas Instruments TI 84 | User Guide - Page 446
Goto label Program Output IS>( IS>( (increment and skip) adds 1 to variable. If the answer is > value cannot be a system variable. :IS>(variable,value) :command (if answer value) :command (if answer > value) Program Output Note: IS>( is not a looping instruction. Chapter 16: Programming 443 - Texas Instruments TI 84 | User Guide - Page 447
:DS - Texas Instruments TI 84 | User Guide - Page 448
name when using RCL. You must paste the name from the PRGM EXEC menu. Return Return quits the subroutine and returns execution to the calling program, even if encountered within nested loops. Any loops are ended. An implied Return exists at the end of any - Texas Instruments TI 84 | User Guide - Page 449
Stop is optional at the end of a program. DelVar DelVar deletes from memory the contents of variable. DelVar variable GraphStyle( GraphStyle( designates the style of the graph to be drawn. function# is the number of the Y= function name in the current graphing mode. graphstyle is a number from 1 to - Texas Instruments TI 84 | User Guide - Page 450
. 7: getKey Checks the keyboard for a keystroke. 8: ClrHome Clears the display. 9: ClrTable Clears the current table. 0: GetCalc( Gets a variable from another TI-84 Plus. A: Get( Gets a variable from CBL 2™ or CBR™. B: Send( Sends a variable to CBL 2 or CBR. Chapter 16: Programming 447 - Texas Instruments TI 84 | User Guide - Page 451
These instructions control input to and output from a program during execution. They allow you to enter values and display answers during program execution. To return to the program editor without selecting an item, press '. Displaying a Graph with Input Input without a variable displays the - Texas Instruments TI 84 | User Guide - Page 452
Input with variable displays a ? (question mark) prompt during execution. variable may be a real number, complex number, list, matrix, string, or Y= function. During program execution, enter a value, which can be an expression, and then press Í. The value is evaluated and stored to variable, and the - Texas Instruments TI 84 | User Guide - Page 453
Displaying the Home Screen Disp (display) without a value displays the home screen. To view the home screen during program execution, follow the Disp instruction with a Pause instruction. Disp Displaying Values and Messages Disp with one or more values displays the value of each. Disp [valueA,valueB - Texas Instruments TI 84 | User Guide - Page 454
but the matrix or list cannot be scrolled. To scroll, use Pause value. DispGraph DispGraph (display graph) displays the current graph. If Pause is encountered after DispGraph, the program halts temporarily so you can examine the screen. Press Í to resume execution. DispTable DispTable (display table - Texas Instruments TI 84 | User Guide - Page 455
. Matrices are displayed in entry format and wrap to the next line. ! is not valid as text. Output(row,column,"text") Output(row,column,value) Program Output For Output( on a Horiz split screen, the maximum value for row is 4. Chapter 16 - Texas Instruments TI 84 | User Guide - Page 456
the key code diagram below. If no key has been pressed, getKey returns 0. Use getKey inside loops to transfer control, for example, when creating video games. Program Output Note and Í were pressed during program execution. Note: You can press É at any time during execution to break the - Texas Instruments TI 84 | User Guide - Page 457
in the table during program execution. GetCalc( GetCalc( gets the contents of variable on another TI-84 Plus and stores it to variable on the receiving TI-84 Plus. variable can be a real or complex number, list element, list name, matrix element, matrix name, string, Y= variable, graph database, or - Texas Instruments TI 84 | User Guide - Page 458
calculators. Get(, Send( Get( gets data from the CBL 2™ or CBR™ and stores it to variable on the receiving TI-84 Plus. variable can be a real number, list element, list name, matrix element, matrix name, string, Y= variable, graph database, or picture. Get(variable) Note: If you transfer a program - Texas Instruments TI 84 | User Guide - Page 459
to execute them from the home screen (Chapter 15). Calling Other Programs as Subroutines Calling a Program from Another Program On the TI-84 Plus, any stored program can be called from another program as a subroutine. Enter the name of the program to use as a subroutine on a line by itself. You can - Texas Instruments TI 84 | User Guide - Page 460
implied Return at the end of the second program. Program Output Subroutine ( ' Notes about Calling Programs Variables are global. label used with Goto and Lbl is local to the program where it is located. label in one program is not recognized by another program. You cannot use Goto to branch to - Texas Instruments TI 84 | User Guide - Page 461
has error(s), it may cause your calculator to reset and lose all data, programs, and applications stored in memory. When you download an assembly language program, it is stored among the other programs as a PRGM menu item. You can: • Transmit it using the TI-84 Plus communication link (Chapter 19 - Texas Instruments TI 84 | User Guide - Page 462
the home screen, press y N and then select AsmComp( to paste it to the screen. 3. Press to display the PRGM EXEC menu. 4. Select the program you want to compile. It will be pasted to the home screen. 5. Press ¢ and then select prgm from the CATALOG. 6. Key in the name you - Texas Instruments TI 84 | User Guide - Page 463
Chapter 17: Activities The Quadratic Formula Entering a Calculation Use the quadratic formula to solve the quadratic equations 3x2 + 5x + 2 more than one instruction on a line. 3. Press 5 ¿ ƒ [B] (above Œ) to store the coefficient of the X term. Press ƒ [:] to enter a new instruction on the same - Texas Instruments TI 84 | User Guide - Page 464
shown on the right side of the display. The cursor moves to the next line, ready for you to enter the next expression. Converting to a Fraction You can show the solution as a fraction. 1. Press to display the MATH menu. Chapter 17: Activities 461 - Texas Instruments TI 84 | User Guide - Page 465
To save keystrokes, you can recall the last expression you entered, and then edit it for a new calculation. 4. Press y [ (above Í) to recall the fraction conversion entry, and then press y [ again to recall the quadratic-formula expression, ------b b---2---------4---a----c2a Chapter 17: Activities - Texas Instruments TI 84 | User Guide - Page 466
edit the quadratic-formula expression to become: ------b b---2----------4---a---c-2a 6. Press Í to find the other solution for the quadratic equation 3x2 + 5x + 2 = 0. Displaying Complex Results Now solve the equation 2x2 N x + 3 = 0. When you set a+bi complex number mode, the TI-84 Plus displays - Texas Instruments TI 84 | User Guide - Page 467
of the X term, and the constant for the new equation are stored to A, B, and C, respectively. 4. Press y [ to recall the store instruction, and then press y [ again to recall the quadratic-formula expression, ------b b---2----------4---a---c-2a 5. Press Í to find one solution for the equation 2x2 - Texas Instruments TI 84 | User Guide - Page 468
find the other solution for the quadratic equation: 2x2 N x + 3 = 0. Note: An alternative for solving equations for real numbers is to use the built-in Equation Solver. Chapter 17: Activities 465 - Texas Instruments TI 84 | User Guide - Page 469
the diagram below. Fold the paper into a box with a lid. What value of X would give your box the maximum volume V? Use the table and graphs to determine the solution. Begin by defining a function that describes the volume of the box. X From the diagram: 2X + A = 20 2X + 2B = 25 V = A...B...X 20 - Texas Instruments TI 84 | User Guide - Page 470
Y1 is selected. Defining a Table of Values The table feature of the TI-84 Plus displays numeric information about a function. You can use a table of values from the function you just defined to estimate an answer to the problem. 1. Press y - (above p) to display the TABLE SETUP menu. 2. Press Í to - Texas Instruments TI 84 | User Guide - Page 471
5. Press and hold † to scroll the table until a negative result for Y1 is displayed. Notice that the maximum length of X for this problem occurs where the sign of Y1 (box's volume) changes from positive to negative, between 10 and 11. 6. Press y -. Notice that TblStart has changed to 6 to - Texas Instruments TI 84 | User Guide - Page 472
2. Press y 0. 3. Press † and } to scroll the table. Notice that the maximum value for Y1 is 410.26, which occurs at X=3.7. Therefore, the maximum occurs where 3.6 - Texas Instruments TI 84 | User Guide - Page 473
the paper at .01-centimeter increments. Setting the Viewing Window You also can use the graphing features of the TI-84 Plus to find the maximum value of a previously defined function. When the graph is activated, the viewing window defines the displayed portion of the coordinate plane. The values - Texas Instruments TI 84 | User Guide - Page 474
The standard window variables define the viewing window as shown. Xmin, Xmax, Ymin, and Ymax define the boundaries of the display. Xscl and Yscl define the distance between tick marks on the X and Y axes. Xres controls resolution. 2. Press 0 Í to define Xmin. 3. Press 20 ¥ 2 to define Xmax using an - Texas Instruments TI 84 | User Guide - Page 475
of Y1=(20N2X)(25à2NX)X is displayed. 2. Press ~ to activate the free-moving graph cursor. The X and Y coordinate values for the position of the graph cursor are displayed on the bottom line. 3. Press |, ~, }, and † to move the freemoving cursor to the apparent maximum of the function. As you move - Texas Instruments TI 84 | User Guide - Page 476
4. Press r. The trace cursor is displayed on the Y1 function. The function that you are tracing is displayed in the top-left corner. 5. Press | and ~ to trace along Y1, one X dot at a time, evaluating Y1 at each X. You also can enter your estimate for the maximum value of X. 6. Press 3 Ë 8. When you - Texas Instruments TI 84 | User Guide - Page 477
Zooming In on the Graph To help identify maximums, minimums, roots, and intersections of functions, you can magnify the viewing window at a specific location using the ZOOM instructions. 1. Press q to display the ZOOM menu. This menu is a typical TI-84 Plus menu. To select an item, you can either - Texas Instruments TI 84 | User Guide - Page 478
p to display the new window settings. Finding the Calculated Maximum You can use a CALCULATE menu operation to calculate a local maximum of a function. 1. Press y / (above r) to display the CALCULATE menu. Press 4 to select 4:maximum. The graph is displayed again with a Left Bound? prompt. 2. Press - Texas Instruments TI 84 | User Guide - Page 479
guess for the maximum. When you press a number key in TRACE, the X= prompt is displayed in the bottomleft corner. Notice how the values for the calculated maximum compare with the maximums found with the free-moving cursor, the trace cursor, and the table. Note: In steps 2 and 3 above, you can enter - Texas Instruments TI 84 | User Guide - Page 480
Comparing Test Results Using Box Plots Problem An experiment found a significant difference between brains, versus their right hands, which are controlled by the left side of their brains. The TI Graphics team conducted a similar test for adult men and women. The test involved 30 small objects, - Texas Instruments TI 84 | User Guide - Page 481
list names WLEFT, WRGHT, MLEFT, and MRGHT, separated by commas. Press Í. The stat list editor now contains only these four lists. 2. Press ... 1 to select 1:Edit. 3. Enter into WLEFT the number of correct guesses each woman made using her left hand (Women Left). Press ~ to move to WRGHT and enter - Texas Instruments TI 84 | User Guide - Page 482
7. Press p. Set Xscl=1 and Yscl=0. Press q 9 to select 9:ZoomStat. This adjusts the viewing window and displays the box plots for the women's results. 8. Press r. Women's left-hand data Women's right-hand data Use | and ~ to examine minX, Q1, Med, Q3, and maxX for each plot. Notice the outlier to - Texas Instruments TI 84 | User Guide - Page 483
11. Compare the right-hand results. Define plot 1 to use WRGHT, define plot 2 to use MRGHT, and then press r to examine minX, Q1, Med, Q3, and maxX for each plot. Who were the better right-hand guessers? In the original experiment boys did not guess as well with right hands, while girls guessed - Texas Instruments TI 84 | User Guide - Page 484
Graphing Piecewise Functions Problem The fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is 50; plus 5 for each kph from 46 to 55 kph; plus 10 for each kph from 56 to 65 kph; plus 20 for each kph from 66 kph and above. Graph the piecewise function that describes the - Texas Instruments TI 84 | User Guide - Page 485
3. Press p and set Xmin=L2, Xscl=10, Ymin=L5, and Yscl=10. Ignore Xmax and Ymax; they are set by @X and @Y in step 4. 4. Press y 5 to return to the home screen. Store 1 to @X, and then store 5 to @Y. @X and @Y are on the VARS Window X/Y secondary menu. @X and @Y specify the horizontal and vertical - Texas Instruments TI 84 | User Guide - Page 486
Graphing Inequalities Problem Graph the inequality 0.4x3 N 3x + 5 < 0.2x + 4. Use the TEST menu operations to explore the values of X where the inequality is true and where it is false. Procedure 1. Press z. Select Dot, Simul, and the default settings. Setting Dot mode changes all graph style icons - Texas Instruments TI 84 | User Guide - Page 487
6. Press o. Turn off Y4, Y5, and Y6. Enter equations to graph only the inequality. 7. Press r. Notice that the values of Y7 and Y8 are zero where the inequality is false. Chapter 17: Activities 484 - Texas Instruments TI 84 | User Guide - Page 488
Solving a System of Nonlinear Equations Problem Using a graph, solve the equation x3N2x=2cos(x). Stated another way, solve the system of two equations and two unknowns: y = x3N2x and y = 2cos(x). Use ZOOM factors to control the decimal places displayed on the graph. Procedure 1. Press z. Select the - Texas Instruments TI 84 | User Guide - Page 489
trace cursor near the intersection. Press Í. What are the coordinates of the intersection point? 8. Press q 4 to select 4:ZDecimal to redisplay the original graph. 9. Press q. Select 2:Zoom In and repeat steps 4 through 8 to explore the apparent function intersection on the left side of the display - Texas Instruments TI 84 | User Guide - Page 490
, the Sierpinski Triangle, and stores the drawing to a picture. To begin, press ~ ~ 1. Name the program SIERPINS, and then press Í. The program editor is displayed. Program PROGRAM:SIERPINS :FnOff :ClrDraw :PlotsOff :AxesOff :0!Xmin:1!Xmax :0!Ymin:1!Ymax :rand!X:rand!Y :For(K,1,3000) :rand!N :If - Texas Instruments TI 84 | User Guide - Page 491
2 à3 - Texas Instruments TI 84 | User Guide - Page 492
Cobweb Attractors Problem Using Web format, you can identify points with attracting and repelling behavior in sequence graphing. Procedure 1. Press z. Select Seq and the default mode settings. Press y .. Select Web format and the default format settings. 2. Press o. Clear all functions and - Texas Instruments TI 84 | User Guide - Page 493
6. Change K to 3.44 and trace the graph to show a cobweb with two attractors. 7. Change K to 3.54 and trace the graph to show a cobweb with four attractors. Chapter 17: Activities 490 - Texas Instruments TI 84 | User Guide - Page 494
A sin(BX) with random integer coefficients between 1 and 10. Try to guess the coefficients and graph your guess as C sin(DX). The program continues until your guess is correct. Program PROGRAM:GUESS :PlotsOff :Func :FnOff :Radian :ClrHome :"Asin(BX)"!Y1 :"Csin(DX)"!Y2 :GraphStyle(1,1) :GraphStyle - Texas Instruments TI 84 | User Guide - Page 495
:Pause :If C=A :Text(1,1,"C IS OK") :If CƒA :Text(1,1,"C IS WRONG") :If D=B :Text(1,50,"D IS OK") :If DƒB :Text(1,50,"D IS WRONG") :DispGraph :Pause Set viewing window. Display graph. Prompt for guess. Display graph. Display results. Display graph. Chapter 17: Activities 492 - Texas Instruments TI 84 | User Guide - Page 496
:If C=A and D=B :Stop :Goto Z Quit if guesses are correct. Chapter 17: Activities 493 - Texas Instruments TI 84 | User Guide - Page 497
Circle and Trigonometric Curves Problem Using parametric graphing mode, graph the unit circle and the sine curve to show the relationship between them. Any function that can be plotted in Func mode can be plotted - Texas Instruments TI 84 | User Guide - Page 498
5. Press r. As the graph is plotting, you may press Í to pause and Í again to resume graphing as you watch the sine function "unwrap" from the unit circle. Note: You can generalize the unwrapping. Replace sin(T) in Y2T with any other trig - Texas Instruments TI 84 | User Guide - Page 499
Finding the Area between Curves Problem Find the area of the region bounded by: f(x) = 300x / (x2 + 625) g(x) = . Y1=300Xà(X2+625) Y2=3cos(.1X) 4. Press y / 5 to select 5:Intersect. The graph is displayed. Select a first curve, second curve, and guess for the intersection toward the left side of - Texas Instruments TI 84 | User Guide - Page 500
5. Press y 5 to go to the home screen. Press y < 7 and use Shade( to see the area graphically. Shade(Y2,Y1,Ans,75) 6. Press y 5 to return to the home screen. Enter the expression to evaluate the integral for the shaded region. fnInt(Y1NY2,X, - Texas Instruments TI 84 | User Guide - Page 501
Using Parametric Equations: Ferris Wheel Problem Problem Using two pairs of parametric equations, determine when two objects in motion are closest to each other in the same plane. A ferris wheel has a diameter (d) - Texas Instruments TI 84 | User Guide - Page 502
to ë X1T and ì X2T, which simulates a chair on the ferris wheel and the ball flying through the air when you press s. 4. Press s to graph the equations. Watch closely as they are plotted. Notice that the ball and the ferris wheel passenger appear to be closest where the paths cross - Texas Instruments TI 84 | User Guide - Page 503
=1 Tmax=3 Tstep=.03 Xmin=0 Xmax=23.5 Xscl=10 Ymin=10 Ymax=25.5 Yscl=10 6. Press r. After the graph is plotted, press ~ to move near the point on the ferris wheel where the paths cross. Notice the values of X, Y, and T. 7. Press † to move to - Texas Instruments TI 84 | User Guide - Page 504
You can use r to, in effect, take snapshots in time and explore the relative behavior of two objects in motion. Chapter 17: Activities 501 - Texas Instruments TI 84 | User Guide - Page 505
Demonstrating the Fundamental Theorem of Calculus Problem 1 Using the functions fnInt( and nDeriv( from the MATH menu to graph functions defined by integrals and derivatives demonstrates graphically that: x F(x) = ∫ dt = ln (x), x > 0 and that 1 Dx ∫1x1-t-dt = 1-x Procedure 1 1. Press z. Select - Texas Instruments TI 84 | User Guide - Page 506
of Y1 and Y2. 5. Press o. Turn off Y1 and Y2, and then enter the numerical derivative of the integral of 1àX and the function 1àX. Set the graph style for Y3 to ç (line) and Y4 to è (thick). 6. Press r. Again, use the cursor keys to compare the values of the two - Texas Instruments TI 84 | User Guide - Page 507
Problem 2 Explore the functions defined by y = ∫ xt2dt , ∫ xt2dt , and ∫ xt2dt 2 0 2 Procedure 2 1. Press o. Turn off all functions and stat plots. Use a list to define these three functions - Texas Instruments TI 84 | User Guide - Page 508
5. Press r. Notice that although the three graphs defined by Y5 are different, they share the same derivative. Chapter 17: Activities 505 - Texas Instruments TI 84 | User Guide - Page 509
Computing Areas of Regular N-Sided Polygons Problem Use the equation solver to store a formula for the area of a regular N-sided polygon, and then solve for each variable, given the other variables. Explore the fact that the - Texas Instruments TI 84 | User Guide - Page 510
from center to vertex of 6 centimeters. 4. Press } } to move the cursor onto A, and then press ă \. The solution for A is displayed on the interactive solver editor. 5. Now solve for B for a given area with various number of sides. Enter A=200 and N=6. To find the distance B, move the cursor onto - Texas Instruments TI 84 | User Guide - Page 511
Xres=1 10. Press o. Turn off all functions and stat plots. Enter the equation for the area. Use X in place of N. Set the graph styles as shown. 11. Press r. After the graph is plotted, press 100 Í to trace to X=100. Press 150 Í. Press 188 Í. Notice that as X increases, the value of Y converges to - Texas Instruments TI 84 | User Guide - Page 512
asymptote to Y1. The area of an N-sided regular polygon, with r as the distance from the center to a vertex, approaches the area of a circle with radius r (pr2) as N gets large. Chapter 17: Activities 509 - Texas Instruments TI 84 | User Guide - Page 513
Computing and Graphing Mortgage Payments Problem You are a loan officer at a mortgage company, and decimal places. Set the other mode settings to the defaults. 2. Press Œ Í Í to display the TVM Solver. Enter these values. Note: Enter a positive number (800) to show PMT as a cash inflow. Payment - Texas Instruments TI 84 | User Guide - Page 514
z. Set Par and Simul. 5. Press o. Turn off all functions and stat plots. Enter these equations and set the graph styles as shown. Note: GPrn( and GInt( are located on the FINANCE menu (APPS 1:FINANCE). 6. Press p. Set these window variables. Tmin=1 Tmax=360 Tstep=12 Xmin=0 Xmax=360 Xscl=10 Ymin - Texas Instruments TI 84 | User Guide - Page 515
payments (Y3T=Y1T+Y2T) is always 800. 8. Press † to move the cursor onto the function for interest defined by X2T and Y2T. Enter 240. The graph shows that for the 240th payment (X=240), 441.97 of the 800 payment is interest (Y=441.97). 9. Press y 5 Œ Í 9 to paste 9:bal( to the home screen - Texas Instruments TI 84 | User Guide - Page 516
At which monthly payment will the principal allocation surpass the interest allocation? Chapter 17: Activities 513 - Texas Instruments TI 84 | User Guide - Page 517
selecting items from the MEMORY menu. To access this menu, press y L. MEMORY 1: About... Displays information about the graphing calculator including current OS version number. 2: Mem Mgmt/Del... Reports memory availability and variable usage. 3: Clear Entries Clears ENTRY (last-entry storage - Texas Instruments TI 84 | User Guide - Page 518
, and data. The available Archive lets you store programs, Apps, groups, and other variables. The App slots are actually individual sectors of Flash ROM where Apps are stored. Graphing calculator TI-84 Plus TI-84 Plus Silver Edition Available RAM 24 Kilobytes 24 Kilobytes Available Archive 491 - Texas Instruments TI 84 | User Guide - Page 519
the type of graphing calculator. Displays the OS version. As new software upgrades become available, you can electronically upgrade your unit. Displays the Product ID. Each Flash-based graphing calculator has a unique product ID, which you may need if you contact technical support. You can also - Texas Instruments TI 84 | User Guide - Page 520
2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu. The TI-84 Plus expresses memory quantities in bytes. 3. Select variable types from the Apps are independent applications which are stored in Flash ROM. AppVars is a variable holder used to store variables created by Apps. You cannot edit - Texas Instruments TI 84 | User Guide - Page 521
To leave the MEMORY MANAGEMENT/DELETE menu, press either y 5 or '. Both options display the home screen. Chapter 18: Memory and Variable Management 518 - Texas Instruments TI 84 | User Guide - Page 522
an Item To increase available memory by deleting the contents of any variable (real or complex number, list, matrix, Y= variable, program, Apps, AppVars, picture, graph database, or string), follow these steps. 1. Press y L to display the MEMORY menu. 2. Select 2:Mem Mgmt/Del to display the MEMORY - Texas Instruments TI 84 | User Guide - Page 523
delete individual variables one by one from this screen. No warning will be given to verify the deletion. Note: If you are deleting programs or Apps, you will receive a message asking you to confirm this delete action. Select 2:Yes to continue. To leave any variable screen without deleting anything - Texas Instruments TI 84 | User Guide - Page 524
. To cancel Clear Entries, press '. Note: If you select 3:Clear Entries from within a program, the Clear Entries instruction is pasted to the program editor, and the Entry (last entry) is cleared when the program is executed. ClrAllLists ClrAllLists sets the dimension of each list in RAM to 0. To - Texas Instruments TI 84 | User Guide - Page 525
list names from memory, from the LIST NAMES menu, or from the stat list editor. Note: If you select 4:ClrAllLists from within a program, the ClrAllLists instruction is pasted to the program editor. The lists are cleared when the program is executed. Chapter 18: Memory and Variable Management 522 - Texas Instruments TI 84 | User Guide - Page 526
programs, or other variables to the user data archive (ARC) where they cannot be edited or deleted inadvertently. Archiving also allows you to free up RAM for variables that may require additional memory. Archived variables cannot be edited and q cannot be archived. Apps and Groups always exist in - Texas Instruments TI 84 | User Guide - Page 527
databases GDB1, GDB2,... yes Graph pictures Pic1, Pic2, ... , Pic9, yes Pic0 Strings Str1, Str2, . . . Str9, Str0 yes Tables TblStart, Tb1, TblInput no Apps Applications AppVars Groups Application variables Variables with minX, maxX, RegEQ, reserved names and others see Note above - Texas Instruments TI 84 | User Guide - Page 528
menu or CATALOG. • Use a Memory Management editor screen. Before archiving or unarchiving variables, particularly those with a large byte size (such as large programs) use the MEMORY menu to: • Find the size of the variable. • See if there is enough free space. For: Archive UnArchive Sizes must - Texas Instruments TI 84 | User Guide - Page 529
To archive or unarchive a list variable (L1) using the Archive/UnArchive options from the MEMORY menu: 1. Press y L to display the MEMORY menu. 2. Select 5:Archive or 6:UnArchive to place the command in the Home screen. 3. Press y d to place the L1 variable in the Home screen. 4. Press Í to - Texas Instruments TI 84 | User Guide - Page 530
2. Select 2:Mem Mgmt/Del to display the MEMORY MANAGEMENT/DELETE menu. 3. Select 4:List to display the LIST menu. 4. Press Í to archive L1. An asterisk will appear to the left of L1 to indicate it is an archived variable. To unarchive a variable in this screen, put the cursor next to the archived - Texas Instruments TI 84 | User Guide - Page 531
5. Press y 5 to leave the LIST menu. Note: You can access an archived variable for the purpose of linking, deleting, or unarchiving it, but you cannot edit it. Chapter 18: Memory and Variable Management 528 - Texas Instruments TI 84 | User Guide - Page 532
defaults on the TI-84 Plus, all defaults in RAM are restored to the factory settings. Stored data and programs are not changed. These are some examples of TI-84 Plus defaults that are restored by resetting the defaults. • Mode settings such as Normal (notation); Func (graphing); Real (numbers); and - Texas Instruments TI 84 | User Guide - Page 533
ALL menu on the TI-84 Plus, follow these steps. 1. Press y L to display the MEMORY menu. 2. Select 7:Reset to display the RAM ARCHIVE ALL menu. Resetting RAM Memory Resetting all RAM restores RAM system variables to factory settings and deletes all nonsystem variables and all programs. Resetting RAM - Texas Instruments TI 84 | User Guide - Page 534
your choice, the message RAM cleared or Defaults set is displayed on the home screen. Resetting Archive Memory When resetting archive memory on the TI-84 Plus, you can choose to delete from user data archive all variables, all applications, or both variables and applications. To reset all or part of - Texas Instruments TI 84 | User Guide - Page 535
2. Select one of the following: 1:Vars to display the RESET ARC VARS menu. 2:Apps to display the RESET ARC APPS menu. 3:Both to display the RESET ARC BOTH menu. 3. Read the message below the menu. • To cancel the reset and return to the HOME screen, - Texas Instruments TI 84 | User Guide - Page 536
displayed on the HOME screen. Resetting All Memory When resetting all memory on the TI-84 Plus, RAM and user data archive memory is restored to factory settings. All nonsystem variables, applications, and programs are deleted. All system variables are reset to default settings. Before you reset all - Texas Instruments TI 84 | User Guide - Page 537
• To continue with the reset, select 2:Reset. The message MEM cleared is displayed on the HOME screen. When you clear memory, the contrast sometimes changes. If the screen is faded or blank, adjust the contrast by pressing y } or †. Chapter 18: Memory and Variable Management 534 - Texas Instruments TI 84 | User Guide - Page 538
Grouping and Ungrouping Variables Grouping Variables Grouping allows you to make a copy of two or more variables residing in RAM and then store them as a group in user data archive. The variables in RAM are not erased. The variables must exist in RAM before they can be grouped. In other words, - Texas Instruments TI 84 | User Guide - Page 539
4. Enter a name for the new group and press Í. Note: A group name can be one to eight characters long. The first character must be a letter from A to Z or q. The second through eighth characters can be letters, numbers, or q. 5. Select the type of data you want to group. You can select 1:All+ which - Texas Instruments TI 84 | User Guide - Page 540
6. Press } and † to move the selection cursor (4) next to the first item you want to copy into a group, and then press Í. A small square will remain to the left of all variables selected for grouping. Repeat the selection process until all variables for the new group are selected and then press ~ - Texas Instruments TI 84 | User Guide - Page 541
Note: You can only group variables in RAM. You cannot group some system variables, such as the last-answer variable Ans and the statistical variable RegEQ. Ungrouping Variables Ungrouping allows you to make a copy of variables in a group stored in user data archive and place them ungrouped in RAM. - Texas Instruments TI 84 | User Guide - Page 542
• When you select 2:Overwrite, the unit overwrites the data of the duplicate variable name found in RAM. Ungrouping resumes. • When you select 3: Overwrite All, the unit overwrites the data of all duplicate variable names found in RAM. Ungrouping resumes. • When you select 4:Omit, the unit does not - Texas Instruments TI 84 | User Guide - Page 543
4. Press } and † to move the selection cursor (4) next to the group variable you want to ungroup, and then press Í. The ungroup action is completed. Note: Ungrouping does not remove the group from user data archive. You must delete the group in user data archive to remove it. Chapter 18: Memory and - Texas Instruments TI 84 | User Guide - Page 544
to cancel the garbage collection process, and then find and correct the errors in your program. When YES is selected, the TI-84 Plus will attempt to rearrange the archived variables to make additional room. Responding to the Garbage Collection Message • To cancel, select 1:No. • If you select 1:No - Texas Instruments TI 84 | User Guide - Page 545
take up to 20 minutes, depending on how much of archive memory has been used to store variables. After garbage collection, depending on how much additional space is freed, the variable may or may not be archived. If not, you can unarchive some variables and try again. Why Is Garbage Collection - Texas Instruments TI 84 | User Guide - Page 546
Each variable that you archive is stored in the first empty block large enough to hold it. This process continues to the end of the last sector. Depending on the size of individual variables, the empty blocks may account for a significant amount of space. Garbage collection occurs when the variable - Texas Instruments TI 84 | User Guide - Page 547
When you unarchive a variable, the Archive free amount increases immediately, but the space is not actually available until after the next garbage collection. If the Archive free amount shows enough available space for your variable, there probably will be enough space to archive it after garbage - Texas Instruments TI 84 | User Guide - Page 548
1. From the HOME screen, press y N to display the CATALOG. 2. Press † or } to scroll the CATALOG until the selection cursor points to the GarbageCollect command or press G to skip to the commands starting with the letter G. 3. Press Í to paste the command to the HOME screen. 4. Press Í to display - Texas Instruments TI 84 | User Guide - Page 549
is displayed, it will indicate the largest single space of memory available for storing a variable and an application. To resolve the problem, use the GarbageCollect command to optimize memory. If memory is still insufficient, you must delete variables or applications to increase space. Chapter - Texas Instruments TI 84 | User Guide - Page 550
introduction. Read the chapter for details. Create and store a variable and a matrix, and then transfer them to another TI-84 Plus. 1. On the home screen of the sending unit, press 5 Ë 5 ¿ ƒ Q. Press Í to store 5.5 to Q. 2. Press y H y H 1 ¢ 2 y I y H 3 ¢ 4 y I y I ¿ y > 1. Press Í to store the - Texas Instruments TI 84 | User Guide - Page 551
screen is displayed. 6. On the sending unit, press Í to archive [A]. An asterisk (ä) will appear, signifying that [A] is now archived. 7. Connect the graphing calculators with the USB unit-to-unit cable. Push both ends in firmly. 8. On the receiving unit, press y 8 ~ to display the RECEIVE menu - Texas Instruments TI 84 | User Guide - Page 552
13. On the sending unit, press ~ to display the TRANSMIT menu. 14. On the sending unit, press 1 to select 1:Transmit and begin transmission. The receiving unit displays the message Receiving....When the items are transmitted, both units display the name and type of each transmitted variable. - Texas Instruments TI 84 | User Guide - Page 553
TI-84 Plus Silver Edition. A USB unit-to-unit cable is included with the TI-84 Plus. The TI-84 Plus also has an I/O port using a I/O unit-to-unit cable to communicate with: • TI-83 Plus Silver Edition • TI-82 • TI-83 Plus • TI-73 • TI-83 • CBL 2™ or a CBR™ Connecting Two Graphing Calculators - Texas Instruments TI 84 | User Guide - Page 554
port. 2. Insert the other end of the cable into the other graphing calculator's I/O port. TI-84 Plus to a TI-83 Plus using I/O Unit-to-Unit Cable The TI-84 Plus I/O link port is located at the top left edge of the graphing calculator. The TI-83 Plus I/O link port is located at the bottom edge of the - Texas Instruments TI 84 | User Guide - Page 555
Linking to a Computer With TI Connect™ software and the USB computer cable that is included with your TI-84 Plus, you can link the graphing calculator to a personal computer. Chapter 19: Communication Link 552 - Texas Instruments TI 84 | User Guide - Page 556
0: Complex... A: Y-Vars... B: String... C: Apps... Displays all items as selected, including RAM and Flash applications. Displays all items as deselected. Displays all program names. Displays all list names. Displays list names L1 through L6. Displays all graph databases. Displays all picture data - Texas Instruments TI 84 | User Guide - Page 557
SendId G: SendOS H: Back Up... Displays all software application variables. Displays all grouped variables. Sends the Calculator ID number immediately. (You do not need to select SEND.) Sends operating system updates to another TI-84 Plus Silver Edition or TI-84 Plus. You can not send the operating - Texas Instruments TI 84 | User Guide - Page 558
Note: An asterisk (ä) to the left of an item indicates the item is archived. 5. Repeat steps 3 and 4 to select or deselect additional items. Sending the Selected Items After you have selected items to send on the sending unit and set the receiving unit to receive, follow these - Texas Instruments TI 84 | User Guide - Page 559
the message Done is displayed on both calculators. Press } and † to scroll through the names. Sending to a TI-84 Plus Silver Edition or TI-84 Plus You can transfer variables (all types), programs, and Flash applications to another TI-84 Plus Silver Edition or TI-84 Plus. You can also backup the RAM - Texas Instruments TI 84 | User Guide - Page 560
archive of the sending TI-84 Plus Silver Edition will be sent to the user data archive of the receiving TI-84 Plus Silver Edition or TI-84 Plus. After sending or receiving data, you can repeat the same transmission to additional TI-84 Plus Silver Edition or TI-84 Plus units-from either the sending - Texas Instruments TI 84 | User Guide - Page 561
through 13 until the items are sent to all additional units. Sending to a TI-83 Plus or TI-83 Plus Silver Edition You can send all variables from a TI-84 Plus to a TI-83 Plus or TI-83 Plus Silver Edition except Flash applications with new features, or programs with new features in them. If archived - Texas Instruments TI 84 | User Guide - Page 562
Receiving Items LINK RECEIVE Menu To display the LINK RECEIVE menu, press y 8 ~. SEND RECEIVE 1: Receive Sets unit to receive data transmission. Receiving Unit When you select 1:Receive from the LINK RECEIVE menu on the receiving unit, the message Waiting... and the busy indicator are displayed. The - Texas Instruments TI 84 | User Guide - Page 563
receiving unit exits receive mode. Receiving from a TI-84 Plus Silver Edition or TI-84 Plus The TI-84 Plus Silver Edition and the TI-84 Plus are totally compatible. Keep in mind, however that the TI-84 Plus has less Flash memory than a TI-84 Plus Silver Edition. Chapter 19: Communication Link 560 - Texas Instruments TI 84 | User Guide - Page 564
TI-83 Plus Silver Edition or TI-83 Plus The TI-84 Plus product family and the TI-83 Plus product family are compatible with a few exceptions. Receiving from a TI-83 You can transfer all variables and programs from a TI-83 to a TI-84 Plus if they fit in the RAM of the TI-84 Plus. The RAM of the TI-84 - Texas Instruments TI 84 | User Guide - Page 565
or archived items) to another TI-84 Plus Silver Edition. You can also backup RAM memory and mode settings to a TI-84 Plus. To perform a RAM memory backup: 1. Use a USB unit-to-unit cable to link two TI-84 Plus units, or a TI-84 Plus and a TI-84 Plus Silver Edition together. 2. On the sending unit - Texas Instruments TI 84 | User Guide - Page 566
menu Note: If a transmission error is returned during a backup, the receiving unit is reset. Memory Backup Complete When the backup is complete, both the sending graphing calculator and receiving graphing calculator display a confirmation screen. Chapter 19: Communication Link 563 - Texas Instruments TI 84 | User Guide - Page 567
between a TI-73, TI-82, TI-83, TI-83 Plus, or TI-83 Plus Silver Edition. • You attempt a data transfer from a TI-84 Plus to a TI-83 Plus, TI-83 Plus Silver Edition, TI-83, TI-82, or TI-73 with variables or features not recognized by the TI-83 Plus, TI-83 Plus Silver Edition, TI-83, TI-82, or TI-73 - Texas Instruments TI 84 | User Guide - Page 568
• You try to use GetCalc( with a TI-83 instead of a TI-84 Plus or TI-84 Plus Silver Edition. Insufficient Memory in Receiving Unit • During transmission, if the receiving unit does not have sufficient memory to receive an item, the Memory Full menu is - Texas Instruments TI 84 | User Guide - Page 569
listed on the right side of the table. From the CATALOG, you can paste any function or instruction to the home screen or to a command line in the program editor. However, some functions and instructions are not valid on the home screen. The items in this table appear in the same order as - Texas Instruments TI 84 | User Guide - Page 570
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item valueA and data archive memory. Asm(assemblyprgmname) Executes an assembly language program. y N Asm( AsmComp(prgmASM1, prgmASM2) Compiles an assembly language program written in ASCII and stores the hex version. y N - Texas Instruments TI 84 | User Guide - Page 571
Function or Instruction/Arguments augment(matrixA, matrixB) augment(listA,listB) AxesOff AxesOn is listB y 9 concatenated to the end of OPS listA. 9:augment( Turns off the graph axes. † y . AxesOff Turns on the graph axes. † y . AxesOn Sets the mode to rectangular complex number mode (a+bi). † - Texas Instruments TI 84 | User Guide - Page 572
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item binompdf(numtrials,p [,x]) , expectedmatrix [,drawflag]) Performs a chi-square test. drawflag=1 draws results; drawflag=0 calculates results. † ... TESTS C:c2LTest( c2GOF-Test(observedlist, expectedlist,df) Performs a test - Texas Instruments TI 84 | User Guide - Page 573
on the clock display y N in the mode screen. ClockOn Sets to 0 the dimension of all lists in memory. y L MEMORY 4:ClrAllLists Clears all drawn elements from a graph or drawing. y < DRAW 1:ClrDraw Clears the home screen. † I/O 8:ClrHome Appendix A: Functions and Instructions 570 - Texas Instruments TI 84 | User Guide - Page 574
Function or Instruction/Arguments ClrList listname1 [,listname2, ..., listname n] ClrTable conj(value) Connected CoordOff CoordOn cos(value) cosL1(value) cosh(value) Result Key or Keys/Menu or Screen/Item Sets to 0 the dimension of one or more listnames. ... EDIT 4:ClrList Clears all values - Texas Instruments TI 84 | User Guide - Page 575
Function or Instruction/Arguments coshL1 (value) CubicReg [Xlistname, Ylistname,freqlist, regequ] cumSum(list) cumSum(matrix) dayOfWk(year,month, day) year must be 4 digits; month and day can be 1 or 2 digit. y N dayOfWk( 1:Sunday 2:Monday 3:Tuesday... Appendix A: Functions and Instructions 572 - Texas Instruments TI 84 | User Guide - Page 576
Function or Instruction/Arguments dbd(date1,date2) value4Dec Degree DelVar variable DependAsk DependAuto det(matrix) DiagnosticOff Result Key or Keys/Menu or Screen/Item Calculates the number of days between date1 and date2 using the actual-daycount method. Π1:Finance CALC D:dbd( Displays a - Texas Instruments TI 84 | User Guide - Page 577
Function or Instruction/Arguments DiagnosticOn dim(listname) dim(matrixname) length!dim(listname) {rows,columns}! matrixname. 3:dim( Displays the home screen. † I/O 3:Disp Displays each value. † I/O 3:Disp Displays the graph. † I/O 4:DispGraph Appendix A: Functions and Instructions 574 - Texas Instruments TI 84 | User Guide - Page 578
Function or Instruction/Arguments DispTable value4DMS Dot DrawF expression DrawInv expression :DS - Texas Instruments TI 84 | User Guide - Page 579
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item Exponent: listâexponent Returns list elements times y D 10 to the Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. ... CALC 0:ExpReg Appendix A: Functions and Instructions 576 - Texas Instruments TI 84 | User Guide - Page 580
Function or Instruction/Arguments ExprOff ExprOn Ücdf(lowerbound, upperbound, numerator df, denominator df) Fill(value,matrixname) Fill(value, -decimal mode for # of decimal places. † z 0123456789 (select one) Sets floating decimal mode. † z Float Appendix A: Functions and Instructions 577 - Texas Instruments TI 84 | User Guide - Page 581
Function or Instruction/Arguments fMax(expression, variable,lower,upper [,tolerance]) fMin(expression,variable, lower,upper[,tolerance]) fnInt(expression Y-VARS 4:On/Off 2:FnOff Selects all Y= functions or specified Y= functions. Y-VARS 4:On/Off 1:FnOn Appendix A: Functions and Instructions 578 - Texas Instruments TI 84 | User Guide - Page 582
of freedom) and denominator df. y = DISTR 9:Üpdf( Displays a real or complex number, expression, list, or matrix as a fraction simplified to its simplest terms. MATH 1:4Frac Sets full screen mode. † z Full Sets function graphing mode. † z Func Appendix A: Functions and Instructions 579 - Texas Instruments TI 84 | User Guide - Page 583
Function or Instruction/Arguments GarbageCollect gcd(valueA,valueB) geometcdf(p,x) geometpdf(p,x) Get(variable) Result Key or Keys/Menu or Screen/ DISTR E:geometpdf( Gets data from the CBL 2™ † or CBR™ System and I/O stores it in variable. A:Get( Appendix A: Functions and Instructions 580 - Texas Instruments TI 84 | User Guide - Page 584
Function or Instruction/Arguments GetCalc(variable [,portflag]) getDate getDtFmt Result Key or Keys/Menu or Screen/Item Gets contents of variable on another TI-84 Plus and stores it to variable on the receiving TI-84 Plus. By default, the TI-84 Plus uses the USB port if it is connected. If the - Texas Instruments TI 84 | User Guide - Page 585
Function or Instruction/Arguments getDtStr(integer) getKey getTime getTmFmt getTmStr(integer) Result Key or Keys/Menu or Screen/Item Returns a string of in the format specified by integer, where: 12 = 12 hour format 24 = 24 hour format y N getTmStr( Appendix A: Functions and Instructions 582 - Texas Instruments TI 84 | User Guide - Page 586
Function or Instruction/Arguments Goto label GraphStyle(function#, graphstyle#) GridOff GridOn G-T Horiz ( Turns off grid format. † y . GridOff Turns on grid format. † y . GridOn Sets graph-table vertical split-screen mode. † z G-T Sets horizontal split-screen † z mode. Horiz Draws a - Texas Instruments TI 84 | User Guide - Page 587
Function or Instruction/Arguments :If condition :Then :commands :End :commands :If condition :Then :commands :Else : . † y Indpnt: Ask Sets table to generate independent-variable values automatically. † y Indpnt: Auto Displays graph. † I/O 1:Input Appendix A: Functions and Instructions 584 - Texas Instruments TI 84 | User Guide - Page 588
Function or Instruction/Arguments Input [variable] Input ["text",variable] Input [Strn,variable] inString(string,substring [,start]) int(value) GInt(pmt1, for a given area under the normal distribution curve specified by m and s. y = DISTR 3:invNorm( Appendix A: Functions and Instructions 585 - Texas Instruments TI 84 | User Guide - Page 589
Function or Instruction/Arguments invT(area,df) iPart(value) irr(CF0,CFList[,CFFreq]) :IS>(variable,value) :commandA :commands isClockOn Ù the next one to five characters as a usercreated list name. y 9 OPS B:Ù Turns off axes labels. † y . LabelOff Appendix A: Functions and Instructions 586 - Texas Instruments TI 84 | User Guide - Page 590
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item LabelOn Turns on axes labels. † y . LabelOn Lbl label Creates a label with frequency freqlist, and stores the regression equation to regequ. ... CALC 8:LinReg(a+bx) Appendix A: Functions and Instructions 587 - Texas Instruments TI 84 | User Guide - Page 591
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item LinReg(ax+b) [Xlistname, Fits a linear regression Ylistname,freqlist, List 4 matr( ln(value) Returns the natural µ logarithm of a real or complex number, expression, or list. Appendix A: Functions and Instructions 588 - Texas Instruments TI 84 | User Guide - Page 592
Function or Instruction/Arguments LnReg [Xlistname, Ylistname,freqlist, regequ] log(value) Logistic [Xlistname, Ylistname,freqlist, regequ] Manual-Fit equname Result Key or Keys/Menu or Screen/Item Fits a logarithmic regression model to Xlistname and Ylistname with frequency freqlist, and stores - Texas Instruments TI 84 | User Guide - Page 593
Function or Instruction/Arguments max(valueA,valueB) max(list) max(listA,listB) max(value,list) mean(list[,freqlist]) median(list[,freqlist]) Med and Ylistname with frequency freqlist, and stores the regression equation to regequ. ... CALC 3:Med-Med Appendix A: Functions and Instructions 590 - Texas Instruments TI 84 | User Guide - Page 594
Function or Instruction/Arguments Menu("title","text1", label1[,...,"text7",label7]) min(valueA,valueB) min(list) min(listA,listB) min(value,list) valueA nCr valueB value nCr list Result Key or Keys/Menu or Screen/Item Generates a menu of up to † seven items during CTL program execution. C: - Texas Instruments TI 84 | User Guide - Page 595
Function or Instruction/Arguments list nCr value listA nCr listB nDeriv(expression, variable,value[,H]) 4Nom(effective rate, compounding normal distribution probability between lowerbound and upperbound for the specified m and s. y = DISTR 2:normalcdf( Appendix A: Functions and Instructions 592 - Texas Instruments TI 84 | User Guide - Page 596
Function or Instruction/Arguments normalpdf(x[,m,s]) not(value) valueA nPr valueB value nPr list list nPr value listA nPr listB npv(interest rate, PRB 2:nPr Computes the sum of the present values for cash inflows and outflows. Π1:Finance CALC 7:npv( Appendix A: Functions and Instructions 593 - Texas Instruments TI 84 | User Guide - Page 597
( Displays value beginning at † specified row and column. I/O 6:Output( Sets parametric graphing † z mode. Par Suspends program execution until you press Í. † CTL 8:Pause Displays value; suspends program execution until you press Í. † CTL 8:Pause Defines Plot# (1, 2, or 3) of type - Texas Instruments TI 84 | User Guide - Page 598
Function or Instruction/Arguments Plot#(type,Xlistname, freqlist) Plot#(type,Xlistname, freqlist,mark) Plot#(type,datalistname, data axis,mark) PlotsOff annuity due, where payments occur at the beginning of each payment period. Π1:Finance CALC F:Pmt_Bgn Appendix A: Functions and Instructions 595 - Texas Instruments TI 84 | User Guide - Page 599
with the specified mean m. y = DISTR C:poissonpdf( Sets polar graphing mode. † z Pol Displays complex value in polar format. CPX 7:4Polar Sets polar graphing coordinates format. † y . PolarGC Executes the program name. † CTRL D:prgm Appendix A: Functions and Instructions 596 - Texas Instruments TI 84 | User Guide - Page 600
a two-proportion † ... z confidence interval. TESTS B:2-PropZInt( Computes a one-proportion † ... z test. alternative=L1 is . drawflag=1 draws results; drawflag=0 calculates results. Appendix A: Functions and Instructions 597 - Texas Instruments TI 84 | User Guide - Page 601
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item 2-PropZTest(x1,n1,x2,n2 [,alternative,drawflag]) Computes a two-proportion z test. alternative=L1 is . drawflag=1 draws results; drawflag=0 calculates results. † ... TESTS 6:2- - Texas Instruments TI 84 | User Guide - Page 602
Function or Instruction/Arguments Pxl-Off(row,column) Pxl-On(row,column) pxl-Test(row,column) P4Rx(r,q) P4Ry(r,q) QuadReg [Xlistname, to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ. ... CALC 5:QuadReg Appendix A: Functions and Instructions 599 - Texas Instruments TI 84 | User Guide - Page 603
Function or Instruction/Arguments QuartReg [Xlistname, Ylistname,freqlist, regequ] Radian rand[(numtrials)] randBin(numtrials,prob [,numsimulations]) randInt( PRB 5:randInt( Returns a random matrix of y > rows (1-99) × columns MATH (1-99). 6:randM( Appendix A: Functions and Instructions 600 - Texas Instruments TI 84 | User Guide - Page 604
Function or Instruction/Arguments randNorm(m,s [,numtrials]) re^qi Real real(value) RecallGDB n numbers. CPX 2:real( Restores all settings stored y < in the graph database STO variable GDBn. 4:RecallGDB Displays the graph and adds the picture stored in Picn. y < STO 2:RecallPic Displays - Texas Instruments TI 84 | User Guide - Page 605
Function or Instruction/Arguments RectGC ref(matrix) :Repeat condition :commands :End :commands Return round(value[,#decimals]) ärow(value,matrix,row) row+(matrix,rowA,rowB) ärow+(value,matrix, rowA,rowB) Result Sets rectangular graphing coordinates format. Returns the row-echelon form of a matrix. - Texas Instruments TI 84 | User Guide - Page 606
, listname2,freqlist1, freqlist2,alternative, drawflag] (Data list input) Performs a two-sample Û test. alternative=L1 is . drawflag=1 draws results; drawflag=0 calculates results. † ... TESTS E:2-SampÜTest Appendix A: Functions and Instructions 603 - Texas Instruments TI 84 | User Guide - Page 607
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item 2-SampÜTest Sx1,n1, Sx2,n2[,alternative, drawflag] (Summary stats input) Performs a two-sample Û test. alternative=L1 is . drawflag=1 draws results; drawflag=0 calculates results. † - Texas Instruments TI 84 | User Guide - Page 608
,listname2, freqlist1,freqlist2, alternative,drawflag]) (Data list input) Computes a two-sample z test. alternative=L1 is . drawflag=1 draws results; drawflag=0 calculates results. † ... TESTS 3:2-SampZTest( Appendix A: Functions and Instructions 605 - Texas Instruments TI 84 | User Guide - Page 609
is . drawflag=1 draws results; drawflag=0 calculates results. † ... TESTS 3:2-SampZTest( Sets scientific notation display mode. † z Sci to end by increment. y 9 OPS 5:seq( Sets sequence graphing mode. † z Seq Appendix A: Functions and Instructions 606 - Texas Instruments TI 84 | User Guide - Page 610
Instruction/Arguments Sequential setDate(year,month,day) setDtFmt(integer) setTime(hour,minute, second) setTmFmt(integer) SetUpEditor Result Key or Keys/Menu or Screen/Item Sets mode to graph L1 through L6 to columns 1 through 6. ... EDIT 5:SetUpEditor Appendix A: Functions and Instructions 607 - Texas Instruments TI 84 | User Guide - Page 611
Function or Instruction/Arguments SetUpEditor listname1 [,listname2,..., listname20] Shade(lowerfunc, upperfunc[, the specified order, starting with column 1. ... EDIT 5:SetUpEditor Draws lowerfunc and y < upperfunc in terms of X on DRAW the current graph and uses 7:Shade( pattern and patres to - Texas Instruments TI 84 | User Guide - Page 612
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item ShadeNorm(lowerbound, degrees of freedom df, and shades the area between lowerbound and upperbound. Simul Sets mode to graph † z functions simultaneously. Simul sin(value) Returns the sine of a real ˜ number, - Texas Instruments TI 84 | User Guide - Page 613
Function or Instruction/Arguments SinReg [iterations, Xlistname,Ylistname, period,regequ] solve(expression, variable,guess, {lower,upper}) SortA(listname) SortA( list. y 9 OPS 1:SortA( Sorts elements of listname in descending order. y 9 OPS 2:SortD( Appendix A: Functions and Instructions 610 - Texas Instruments TI 84 | User Guide - Page 614
of the elements in MATH list with frequency freqlist. 7:stdDev( Stop Ends program execution; returns to home screen. † CTL F:Stop Store: value!variable Stores value in variable. ¿ StoreGDB n Stores current graph in database GDBn. y < STO 3:StoreGDB StorePic n Stores current picture in - Texas Instruments TI 84 | User Guide - Page 615
Function or Instruction/Arguments sub(string,begin,length) sum(list[,start,end]) tan(value) tanL1(value) Tangent(expression, value) tanh( distribution probability between lowerbound and upperbound for the specified degrees of freedom df. y = DISTR 6:tcdf( Appendix A: Functions and Instructions 612 - Texas Instruments TI 84 | User Guide - Page 616
Function or Instruction/Arguments Text(row,column,text1, text2,...,text n) Then See If:Then Time timeCnv(seconds) TInterval [listname, freqlist,confidence level] (Data list input) TInterval v,Sx,n [,confidence level] (Summary stats input) Result Writes text on graph beginning at pixel (row,column), - Texas Instruments TI 84 | User Guide - Page 617
of freedom df. y = DISTR 5:tpdf( Displays the graph and enters TRACE mode. r Performs a t test with frequency freqlist. alternative=L1 is . drawflag=1 draws results; drawflag=0 calculates results. † ... TESTS 2:T-Test Performs a t test with frequency - Texas Instruments TI 84 | User Guide - Page 618
the user data archive memory to RAM. To archive variables, use Archive. y L 6:UnArchive Sets sequence graphs to † y . plot u(n) on the x-axis and uv v(n) on the y-axis. Sets sequence graphs to † y . plot u(n) on the x-axis and uw w(n) on the y-axis. Appendix A: Functions and Instructions 615 - Texas Instruments TI 84 | User Guide - Page 619
variance( Draws a vertical line at x. y < DRAW 4:Vertical Sets sequence graphs to † y . plot v(n) on the x-axis and vw w(n) on the y-axis. Sets sequence graphs to † y . trace as webs. Web Executes commands while condition is true. † CTL 5:While Appendix A: Functions and Instructions 616 - Texas Instruments TI 84 | User Guide - Page 620
Function or Instruction/Arguments valueA xor valueB ZBox ZDecimal ZInteger ZInterval s[,listname, freqlist, = 0. valueA and valueB can be real numbers, expressions, or lists. y : LOGIC 3:xor Displays a graph, lets you draw a box that defines a new viewing window, and updates the window. † q ZOOM - Texas Instruments TI 84 | User Guide - Page 621
Function or Instruction/Arguments Zoom In Zoom Out ZoomFit ZoomRcl ZoomStat ZoomSto Result Key or Keys/Menu or Screen/Item Magnifies the part of the graph that surrounds the cursor location. † q ZOOM 2:Zoom In Displays a greater portion of the graph, centered on the cursor location. † q ZOOM - Texas Instruments TI 84 | User Guide - Page 622
Replots the graph using the † q window variables of the MEMORY graph that was displayed 1:ZPrevious before you executed the last ZOOM instruction. Adjusts the =1 is >. drawflag=1 draws results; drawflag=0 calculates results. † ... TESTS 1:Z-Test( Appendix A: Functions and Instructions 619 - Texas Instruments TI 84 | User Guide - Page 623
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item Z-Test(m0,s,v,n [,alternative,drawflag]) (Summary stats input) Performs a z test. alternative=L1 is . drawflag=1 draws results; drawflag=0 calculates results. † ... TESTS 1:Z-Test( - Texas Instruments TI 84 | User Guide - Page 624
Function or Instruction/Arguments Transpose: matrixT xthrootx‡value xthrootx‡list listx‡value listAx‡listB Cube: value3 Cube root: 3‡(value) Result . MATH 3:3 Returns the cube root of a real or complex number, expression, or list. MATH 4:3‡( Appendix A: Functions and Instructions 621 - Texas Instruments TI 84 | User Guide - Page 625
Function or Instruction/Arguments Equal: valueA=valueB Not equal: valueAƒvalueB Less than: valueAvalueB . Returns 0 if valueA valueB. valueA and valueB can be real or complex numbers, expressions, or lists. y : TEST 3:> Appendix A: Functions and Instructions 622 - Texas Instruments TI 84 | User Guide - Page 626
Function or Instruction/Arguments Less than or equal: valueAvalueB Greater than or equal: valueA,valueB Inverse: valueL1 Inverse: listL1 real or complex number or expression. Returns list elements ¡ squared. Returns matrix multiplied by ¡ itself. Appendix A: Functions and Instructions 623 - Texas Instruments TI 84 | User Guide - Page 627
Function or Instruction/Arguments Powers: value^power Powers: list^power Powers: value^list Powers: matrix^power Negation: Lvalue Power of ten: . Returns square root of a real or complex number, expression, or list. y C Returns valueA times ¯ valueB. Appendix A: Functions and Instructions 624 - Texas Instruments TI 84 | User Guide - Page 628
or Instruction/Arguments Multiplication: valueälist Multiplication: listävalue Multiplication: listAälistB Multiplication: valueämatrix Multiplication: matrixAämatrixB Division: valueAàvalueB Division: listàvalue Division: valueàlist Division: listAàlistB Addition: valueA+valueB Addition: list - Texas Instruments TI 84 | User Guide - Page 629
Function or Instruction/Arguments Result Key or Keys/Menu or Screen/Item Addition: matrixA+matrixB Returns matrixA elements à plus matrixB elements. Concatenation: string1+string2 Concatenates two or more à strings. Subtraction: valueANvalueB Subtracts valueB from ¹ valueA. Subtraction: - Texas Instruments TI 84 | User Guide - Page 630
to specific data types. The variables A through Z and q are defined as real or complex numbers. You may store to them. The TI-84 Plus can update X, Y, R, q, and T during graphing, so you may want to avoid using these variables to store nongraphing data. The variables (list names) L1 through L6 are - Texas Instruments TI 84 | User Guide - Page 631
up RAM for variables that may require additional memory. The names of archived variables "*" are preceded by an asterisk indicating they are in user data archive. System Variables The variables below must be real numbers. You may store to them. Since the TI-84 Plus can update some of them, as the - Texas Instruments TI 84 | User Guide - Page 632
Statistics Formulas This section contains statistics formulas for the Logistic and SinReg regressions, ANOVA, 2-SampÜTest, and 2-SampTTest. Logistic The logistic regression algorithm applies nonlinear recursive least-squares techniques to optimize the following cost function: ∑ J = i N = 1 ⎛ - Texas Instruments TI 84 | User Guide - Page 633
SinReg The sine regression algorithm applies nonlinear recursive least-squares techniques to optimize the following cost function: N ∑ J = [a sin(bxi + c) + d - yi]2 i=1 which is the sum of the squares of the residual errors, where: x = the independent variable list y = the dependent variable - Texas Instruments TI 84 | User Guide - Page 634
The mean squares (MS) that make up Ü are: FactorMS = F-----a---c---t--o---r---S---S-Factordf ErrorMS = E-----r--r---o---r---S---S-Errordf The sum of squares (SS) that make up the mean squares are: I ∑ FactorSS = ni(xi-x)2 i=1 I ∑ ErrorSS = (ni-1)Sxi2 i=1 The degrees of freedom df that make - Texas Instruments TI 84 | User Guide - Page 635
2-SampFTest Below is the definition for the 2-SampÜTest. Sx1, Sx2 = Sample standard deviations having n1-1 and n2-1 degrees of freedom df, respectively. Ü = Û-statistic = ⎛ ⎝ SS----xx---12-⎠⎞ 2 df(x, n1-1 , n2-1 ) = Ûpdf( ) with degrees of freedom df, n1-1 , and n2-1 p = reported p value - Texas Instruments TI 84 | User Guide - Page 636
2-SampÜTest for the alternative hypothesis s1 ƒ s2. Limits must satisfy the following: Lbnd ∞ p-- = 2 ∫ f(x,n1 - 1,n2 - 1)dx = ∫ f(x,n1 - 1,n2 - 1)dx 0 Ubnd where: [Lbnd,Ubnd] = lower and upper limits The Ü-statistic is used as the bound producing the smallest integral. The remaining bound - Texas Instruments TI 84 | User Guide - Page 637
where the computation of S and df are dependent on whether the variances are pooled. If the variances are not pooled: S = S----x---1--2- + -S---x---2--2n1 n2 ⎛ ⎜ S----x---1--2- + -S---x---2--2-⎟⎞ 2 df n----1 n----2 ------1-------n1 - 1 ⎛ ⎜ ⎝ -S--n-x---11--2-⎠⎟⎞ 2 + ------1-------n2 - Texas Instruments TI 84 | User Guide - Page 638
Financial Formulas This section contains financial formulas for computing time value of money, amortization, cash flow, interest-rate conversions, and days between dates. Time Value of Money i = [e(y × ln(x + 1))]-1 where PMT ƒ 0 : y = C/Y ÷ P/Y x = (.01 × I%) ÷ C/Y C/Y = compounding periods - Texas Instruments TI 84 | User Guide - Page 639
The iteration used to compute i: 0 = PV + PMT × Gi 1 1----+-----i--)------N-i + FV × (1 + i)-N I% = 100 × C ⁄ Y × [e(y × ln(x + 1)) - 1] where: x = i y = P/Y ÷ C/Y Gi = 1 + i × k where: k = 0 for end-of-period payments k = 1 for beginning-of-period payments N = -l--n PP--------MM - Texas Instruments TI 84 | User Guide - Page 640
where: i = 0 PMT = -----i- × PV + ----P----V-----+-----F----V----- Gi (1 + i)N - 1 where: i ƒ 0 PMT = -(PV + FV) ÷ N where: i = 0 PV = -P----M-----T-----×----G-----i - FV 1--------- - P-----M-----T-----×-----G----i i (1 + i)N i where: i ƒ 0 PV = -(FV + PMT × N) where: i = 0 FV = - Texas Instruments TI 84 | User Guide - Page 641
Amortization If computing bal(), pmt2 = npmt Let bal(0) = RND(PV) Iterate from m = 1 to pmt2 ⎧ Im = RND[RND12(-i × bal(m - 1))] ⎩⎨bal(m) = bal(m - 1) - Im + RND(PMT) then: bal( ) = bal(pmt2) ΣPrn( ) = bal(pmt2) - bal(pmt1) ΣInt( ) = (pmt2 - pmt1 + 1) × RND(PMT) - ΣPrn( ) where: RND = round the - Texas Instruments TI 84 | User Guide - Page 642
Cash Flow ∑ npv( ) = CF0 + N C Fj ( 1 + i - ) Sj - 1 (1 - (1 + i)-nj i j=1 where: ⎧ ⎪ j ∑ Sj = ⎪ ⎨ ni ⎪i = 1 ⎪ ⎩ 0 j≥1 j=0 Net present value is dependent on the values of the initial cash flow (CF0), subsequent cash flows (CFj), frequency of each cash flow (nj), and the - Texas Instruments TI 84 | User Guide - Page 643
4Nom = 100 × CP × [e1 ÷ CP × ln(x + 1) - 1 ] where: x = .01 × Eff Eff = effective rate CP = compounding periods Nom = nominal rate Days between Dates With the dbd( function, you can enter or compute a date within the range Jan. 1, 1950, through Dec. 31, 2049. Actual/actual day-count method ( - Texas Instruments TI 84 | User Guide - Page 644
+ (number of days MB to M2) + DT2 + (---Y----2----------Y---B----)- 4 where: M1 DT1 Y1 M2 DT2 Y2 MB DB YB = month of first date = day of first date = year of first date = month of second date = day of second date = year of second date = base month (January) = base day (1) = base year (first year - Texas Instruments TI 84 | User Guide - Page 645
TI-84 Plus TI-84 Plus Results There may be a number of reasons that your TI-84 Plus is not displaying the expected results; however, the most common solutions involve order of operations or mode settings. Your calculator multiplication, and division 6. Addition and subtraction 7. Relational functions - Texas Instruments TI 84 | User Guide - Page 646
3. Press Í to save the angle mode setting. ERR:DIM MISMATCH Error Your TI-84 Plus displays the ERR:DIM MISMATCH error if you are trying to perform an operation The ERR:INVALID DIM error message may occur if you are trying to graph a function that does not involve the stat plot features. The error can - Texas Instruments TI 84 | User Guide - Page 647
About. Your unique product ID code Backups Your TI-84 Plus is similar to a computer, in that it stores files and Apps that are important to you. It is always a good idea to back up your graphing calculator device files and Apps using the TI Connect™ software and a USB computer cable. You can find - Texas Instruments TI 84 | User Guide - Page 648
Apps TI-84 Plus Software Applications (Apps) is software that you can add to your calculator in the same way you would add software to your computer. Apps let you customize your calculator for peak performance in specific areas of study. You can find apps for the TI-84 Plus at the TI Online Store at - Texas Instruments TI 84 | User Guide - Page 649
the TI-84 Plus detects an error, it returns an error message as a menu title, such as ERR:SYNTAX or ERR:DOMAIN. This table contains each error type, possible causes, and suggestions for correction. The error types listed in this table are each preceded by ERR: on your graphing calculator display - Texas Instruments TI 84 | User Guide - Page 650
equation solver, you specified a guess that is not between lower and upper. • Your guess and several points around it are undefined. Examine a graph of (, or the equation solver, you entered lower , upper. You pressed the É key to break execution of a program, to halt a DRAW instruction, or to stop - Texas Instruments TI 84 | User Guide - Page 651
Duplicate Name EXPIRED Possible Causes and Suggested Remedies Your calculator displays the ERR:DIM MISMATCH error if you are to a function or instruction outside the valid range. This error is not returned during graphing. The TI-84 Plus allows for undefined values on a graph. See Appendix A. - Texas Instruments TI 84 | User Guide - Page 652
than L1 through L6) from a TI-84 Plus to a TI.82. • You attempted to transfer L1 through L6 from a TI-84 Plus to a TI.82 without using 5:Lists to TI82 on the LINK SEND menu. This error occurs when the SendID command is executed but the proper graphing calculator ID cannot be found. • You attempted - Texas Instruments TI 84 | User Guide - Page 653
a variable or function that was transferred from the TI.82 and is not valid for the TI-84 Plus For example, you may have transferred UnN1 to the TI-84 Plus from the TI.82 and then tried to reference it. • In Seq mode, you attempted to graph a phase plot without defining both equations of the - Texas Instruments TI 84 | User Guide - Page 654
in the Goto instruction is not defined with a Lbl instruction in the program. Memory is insufficient to perform the instruction or function. You must delete items from memory before executing the instruction or function. Recursive problems return this error; for example, graphing the equation Y1 - Texas Instruments TI 84 | User Guide - Page 655
. This error is not returned during graphing. The TI-84 Plus allows for undefined values on a graph. You attempted to enter, or you have calculated, a number that is beyond the range of the graphing calculator. This error is not returned during graphing. The TI-84 Plus allows for undefined values on - Texas Instruments TI 84 | User Guide - Page 656
L1. • The SinReg instruction or a polynomial regression generated a singular matrix (determinant = 0) because it could not find a solution, or a solution does not exist. This error is not returned during graphing. The TI-84 Plus allows for undefined values on a graph. SINGULARITY expression in the - Texas Instruments TI 84 | User Guide - Page 657
, arguments, parentheses, or commas. Appendix A displays the arguments and punctuation needed to execute the function or instruction. For example, stdDev(list[,freqlist]) is a function of the TI-84 Plus. The arguments are shown in italics. The arguments in brackets are optional and you need not type - Texas Instruments TI 84 | User Guide - Page 658
attempted to receive an incompatible variable version from another graphing calculator. A problem exists with the window variables. • You defined small or too large to graph correctly. You may have attempted to zoom in or zoom out to a point that exceeds the TI-84 Plus's numerical range. • A point - Texas Instruments TI 84 | User Guide - Page 659
Computational Accuracy To maximize accuracy, the TI-84 Plus carries more digits internally than it a value for @X from the home screen or a program in Full screen mode, Xmax is calculated as Xmin + @X É... 94. In G-T split-screen mode, Xmax is calculated as Xmin + @X É... 46. Ymin is the center - Texas Instruments TI 84 | User Guide - Page 660
you enter a value for @Y from the home screen or a program in Full screen mode, Ymax is calculated as Ymin + @Y É... 62. In Horiz split-screen mode, Ymax is calculated as Ymin + @Y ... 30. In G-T split-screen mode, Ymax is calculated as Ymin + @Y É ... 50. Cursor coordinates are displayed as eight - Texas Instruments TI 84 | User Guide - Page 661
Function sinh x, cosh x tanh x sinhL1 x coshL1 x tanhL1 x ‡x (real mode) ‡x (complex mode) x! Range of Input Values |x| 230.25850929940 |x| < 10100 |x| < 5 × 1099 1 x < 5 × 1099 L1 < x < 1 0 x < 10100 |x| < 10100 L.5 _x 69, where x is a multiple of .5 Function Results Function sinL1 x, - Texas Instruments TI 84 | User Guide - Page 662
and Warranty Information Texas Instruments Support and Service For general information Home Page: KnowledgeBase and e-mail inquiries: Phone: International information: education.ti.com education.ti.com/support (800) TI-CARES / (800) 842-2737 For U.S., Canada, Mexico, Puerto Rico, and Virgin - Texas Instruments TI 84 | User Guide - Page 663
Virgin Islands: Always contact Texas Instruments Customer Support before returning a product for service. All other customers: Refer to the leaflet enclosed with this product (hardware) or contact your local Texas Instruments retailer/distributor. Appendix C: Service and Warranty Information 660 - Texas Instruments TI 84 | User Guide - Page 664
quality (at TI's option) when the product is returned, postage prepaid, to Texas Instruments Service Facility. The warranty TI strongly recommends that you insure the product for value prior to mailing. Software. Software is licensed, not sold. TI and its licensors do not warrant that the software - Texas Instruments TI 84 | User Guide - Page 665
the original purchase date. Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction. This warranty is void if the product has been damaged by accident or unreasonable use, neglect, improper service, or other causes not arising out of - Texas Instruments TI 84 | User Guide - Page 666
All Other Customers For information about the length and terms of the warranty, refer to your package and/or to the warranty statement enclosed with this product, or contact your local Texas Instruments retailer/distributor. Appendix C: Service and Warranty Information 663 - Texas Instruments TI 84 | User Guide - Page 667
. The silver oxide battery provides auxiliary power to retain memory while you replace the AAA batteries. When the battery voltage level drops below a usable level, the TI-84 Plus: Displays this message when Displays this message when you attempt you turn on the unit. to download an application - Texas Instruments TI 84 | User Guide - Page 668
Effects of Replacing the Batteries Do not remove both types of batteries (AAA and silver oxide) at the same time. Do not allow the batteries to lose power or dismantle batteries. Replacing the Batteries To replace the batteries, follow these steps. Appendix C: Service and Warranty Information 665 - Texas Instruments TI 84 | User Guide - Page 669
Replace the cover and secure it with the screw. Use a SR44SW or 303 (or equivalent) silver oxide battery. 4. Replace the battery compartment cover. Turn the graphing calculator on and adjust the display contrast, if necessary, by pressing y } or †. Appendix C: Service and Warranty Information 666 - Texas Instruments TI 84 | User Guide - Page 670
anything on the screen, you may need to adjust the graphing calculator contrast. To darken the screen, press and release y, busy indicator (dotted line) is displayed, a graph or program has been paused; the TI-84 Plus is waiting for input. Press Í to continue C: Service and Warranty Information 667 - Texas Instruments TI 84 | User Guide - Page 671
TI-84 Plus does not function even though you are sure that the batteries are fresh, you can try manually resetting it. • Remove all of the AAA batteries from the graphing calculator All nonsystem variables, applications (Apps), and programs are deleted. • Press y Service and Warranty Information 668 - Texas Instruments TI 84 | User Guide - Page 672
Appendix C: Service and Warranty Information 669 - Texas Instruments TI 84 | User Guide - Page 673
84, 626 (( ) (parentheses 41 () (plot type, normal probability) . . . 322 ()Int( (sum of interest 585 ()Prn( (sum of principal 597 (* (multiplication 53, 624 (* (plot type, modified box 320 (*f(x)dx operation on a graph 131 (*row 244, 602 (*row 602 (+ (addition (4Frac (to fraction 57, 579 ( - Texas Instruments TI 84 | User Guide - Page 674
of interest 585 )Prn( (sum of principal 597 bal( (amortization balance) . 399, 568 calculating schedules 399 formula 638 and (Boolean operator 90, 567 ANGLE menu 84 angle modes 22 angle 77, 567 animate graph style 101 ANOVA( (one-way variance analysis) . . . 366 567, 630 Ans (last answer - Texas Instruments TI 84 | User Guide - Page 675
(tan 53 Asm 458, 567 AsmComp 458, 567 AsmPrgm 458, 567 assembly language programs . . . . . 458 augment 240, 267, 568 Automatic Power Down (APD , 568 B backing up calculator memory . 556, 562 bal( (amortization balance) . . . . 399, 568 batteries 5, 664 below graph style 101 binomcdf 380, - Texas Instruments TI 84 | User Guide - Page 676
compiling an assembly program 458, 567 calculators 550, 551, 558 contact information 659 contrast (display 6 convergence, sequence graphing . . 167 conversions 4Dec (to decimal 57, 573 4DMS (to degrees/minutes/ seconds) 86 575 4Eff (to effective interest rate) . . . 402 4Frac (to fraction - Texas Instruments TI 84 | User Guide - Page 677
. 242, 263 cumulative sum (cumSum 572 cursors 9, 19 customer support and service . . . . . 659 D Data input option 336, 337 143 defragmenting 541 Degree angle mode 22, 84, 573 degrees notation 85, 620 delete 574 Disp (display 450, 574 DispGraph (display graph) . . . . 451, 574 display contrast - Texas Instruments TI 84 | User Guide - Page 678
instructions Shade_t 384, 609 Shade 385, 608 ShadeF 385, 608 ShadeNorm 383, 609 division 53, 625 ∆List 263, 588 DMS (degrees/minutes/seconds entry notation 84, 626 Dot (plotting mode 23, 575 dot graph System (EOS) . . . 40 Equation Solver 61 equations with multiple roots 66 errors - Texas Instruments TI 84 | User Guide - Page 679
of values 467 setting the viewing window 470 tracing the graph 472 zooming in on the graph 474 zooming in on the table 468 cobweb attractors 489 fundamental problem 498 piecewise functions 481 quadratic formula converting to a fraction 461 displaying complex results 463 entering a calculation - Texas Instruments TI 84 | User Guide - Page 680
, 579 full-screen mode (Full 24, 579 Func (function graphing mode) . . 23, 579 function graphing accuracy 114 CALC (calculate menu 126 defining and displaying 94 defining in the Y= editor 96 defining on the home screen, in a program 98 deselecting 99 displaying 94, 105, 111 ∆X and ∆Y window - Texas Instruments TI 84 | User Guide - Page 681
541 GarbageCollect 543, 580 gcd( (greatest common divisor) . 71, 580 GDB (graph database 207 geometcdf 382, 580 geometpdf 381, 580 Get( (get data from CBL 2™ or CBR™) . 455 580 GetCalc( (get data from TI-84 Plus) 454, 581 getDate, get current date 581 getDtFmt, get date format 581 getDtStr - Texas Instruments TI 84 | User Guide - Page 682
I% (annual interest rate variable) . . . 391, 406 identity 239, 583 If instructions If 437, 583 If-Then 437, 584 If-Then-Else 438, 584 imag( ( calculating test results (Calculate) . . 339 confidence interval calculations . 339 data input or stats input 337 entering argument values 337 graphing - Texas Instruments TI 84 | User Guide - Page 683
labels graph 110, 586 program 442, graph style 101 line segments, drawing 189 Line( (draw line 190, 587 lines, drawing 190, 191 LINK RECEIVE menu 559 LINK SEND menu 553 linking receiving items 559 to a CBL 2™ or CBR 551 to a PC or Macintosh 552 to a TI-84 Plus Silver Edition or TI-84 Plus - Texas Instruments TI 84 | User Guide - Page 684
and displaying 249 using in expressions 256 using to graph a family of curves 112, 251 using with math (regression 311, 589 logistic regression formula 629 M Manual 313 Manual Linear Fit 306, 313 marked for deletion 542 . . . . . 224 editing matrix elements 226 indicator 228 inverse 233 - Texas Instruments TI 84 | User Guide - Page 685
EDIT menu 223 MATRX MATH menu 236 MATRX NAMES menu 228 max( (maximum 70, 270, 590 maximum of a function (fMax 59 maximum of a function (fMax( ) . . . . 578 maximum operation on a graph (fMin 578 minimum operation on a graph . . . . . 129 minutes notation 84, 626 ModBoxplot plot type 320 mode - Texas Instruments TI 84 | User Guide - Page 686
conversions 86, 599 panning 117 Par/Param (parametric graphing mode) . 23 594 parametric equations 138 parametric graphing CALC (calculate operations on a graph 143 defining and editing 138 free-moving cursor 141 graph format 139 graph styles 137 moving the cursor to a value . . . . 142 - Texas Instruments TI 84 | User Guide - Page 687
151 PolarGC (polar graphing coordinates) . . . 109 596 pooled option 336, 338 power 54, 624 power of ten (10 54 power of ten (10 624 present value 391, 395 previous entry (Last Entry 29 prgm (program name 445, 596 PRGM CTL (program control menu) . 435 PRGM EDIT menu 434 PRGM EXEC - Texas Instruments TI 84 | User Guide - Page 688
new 427 defined 427 deleting 428 deleting command lines 433 editing 432 entering command lines 430 executing 431 inserting command lines 433 instructions 435 name (prgm 445, 596 renaming 433 running assembly language program 458 stopping 432 subroutines 456 Prompt 450, 597 Pt-Change - Texas Instruments TI 84 | User Guide - Page 689
a program 100 functions in the Y= editor 100 stat plots from the Y= editor . . . . 100 Send( (send to CBL 2™ or CBR™) . 455, 606 SendID 554 sending See transmitting 52 SendSW 554 Seq (sequence graphing mode) . 23, 606 seq( (sequence 262, 606 sequence graphing axes format 161 CALC (calculate - Texas Instruments TI 84 | User Guide - Page 690
TI-84 Plus versus TI-82 table . . . 173 tracing 162 web plots 165 window variables 159 Y= editor 155 ZOOM (zoom menu 164 Sequential (graphing order mode) . . . 23, 607 service and support , 610 Smart Graph 111 solve 66, 610 Solver 61 solving for variables in the equation solver 64 SortA( - Texas Instruments TI 84 | User Guide - Page 691
from list names . 292 displaying 283 edit-elements context 296 editing elements of formula-generated lists 293 editing list elements 288 entering list names 284 318 Boxplot (regular box plot 321 defining 322 from a program 326 Histogram 320 ModBoxplot (modified box plot) . 320 NormProbPlot - Texas Instruments TI 84 | User Guide - Page 692
611 StoreGDB 208, 611 StorePic 206, 611 storing graph databases (GDBs 208 graph pictures 205 variable values 27 String4Equ( (string-to-equation subroutines 445 subtraction 53, 626 sum( (summation 271, 612 support and service 659 system variables 628 T T (transpose matrix 237, 621 TABLE - Texas Instruments TI 84 | User Guide - Page 693
110, 116 Trace instruction in a program . 118, 614 transmitting error conditions 564 from a TI-83 562 from a TI-83 Plus Silver Edition or TI-83 Plus 562 from a TI-84 Plus Silver Edition or TI-84 Plus 562 stopping 556 to a TI-84 Plus Silver Edition or TI-84 Plus 556 transpose matrix (T 237 - Texas Instruments TI 84 | User Guide - Page 694
axes 110 calculator 4 coordinates 109 expressions 110 functions 100 grid v sequence function 154 value operation on a graph 126 variables complex 25 displaying and storing values . . . . 27 equation solver 64 graph databases 25 graph pictures 25 independent/dependent 180 list 25, 247 - Texas Instruments TI 84 | User Guide - Page 695
(one-sample z confidence interval 352, 617 zoom 118, 119, 120, 121, 122, 123, 124, 125 cursor 119 factors 124 function graphing 118 parametric graphing 143 polar graphing 151 sequence graphing 164 Zoom In (zoom in 120, 618 ZOOM MEMORY menu 123 ZOOM menu 118 Zoom Out (zoom out 120, 618 - Texas Instruments TI 84 | User Guide - Page 696
ZPrevious (use previous window) . . . 619 ZSquare (set square pixels) . . . 121, 619 ZStandard (use standard window) . . 122, 619 Z-Test (one-sample z test) . . . . 342, 619 ZTrig (trigonometric window) . . 122, 620 Index 693
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TI-84 Plus
TI-84 Plus Silver Edition
Guidebook