Texas Instruments TI-36X Pro User Manual
Texas Instruments TI-36X Pro Manual
The manual viewer requires the flash plugin to be installed and enabled.
To view this page ensure that Adobe Flash Player version 10 or greater is installed.
Texas Instruments TI-36X Pro manual table of contents:
-
Page 1
TI-36X Pro Calculator Important information...2 Examples ...3 Switching the calculator on and off ...3 Display contrast ...3 Home screen ...3 2nd functions ...5 Modes ...5 Multi-tap keys...8 Menus ...8 Scrolling expressions and history ...9 Answer toggle...10 Last answer ...10 ... -
Page 2
... Conversions...66 Complex numbers...69 Errors...71 Battery information...76 In case of difficulty ...77 Texas Instruments Support and Service...78 ... materials available solely on an "as-is" basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental... -
Page 3
...(Automatic Power Down™) feature turns off the calculator automatically if no key is pressed ... contrast of the display can depend on room lighting, battery freshness, and viewing angle. To adjust ...instructions. The answers are displayed on the Home screen. The TI-36X Pro screen can display a maximum ... -
Page 4
... you calculate an entry on the Home screen, depending upon space, the answer is displayed either ...Fixed-decimal setting. (See Mode section.) Scientific or engineering notation. (See Mode section... indicator displayed for default DEC mode. The calculator is performing an operation. 56 An entry is stored... -
Page 5
... the secondary function of a given key. Notice that 2ND appears as an indicator on the screen. To cancel it before entering data, press % again. For example, % b 25 < calculates the square root of 25 and returns the result, 5. Modes q Use q to choose modes. Press $ # ! " to choose a mode, and < to ... -
Page 6
... power is always a multiple of 3. Note: E is a shortcut key to enter a number in scientific notation format. The result displays in the numeric notation format selected in ... results DEC HEX BIN OCT Sets the number base used for calculations. DEC decimal HEX hexadecimal (To enter hex digits A through ... -
Page 7
Examples of Classic and MathPrint™ modes Classic mode Sci MathPrint™ mode Sci Float mode and answer toggle key. Float mode and answer toggle key. Fix 2 Fix 2 and answer toggle key. U n/d U n/d Exponent example Exponent example Square root example Square root example Cube root example... -
Page 8
... include z, X, Y, Z, C, D, H, and g. Applicable sections of this guidebook describe how to use the keys. Menus Menus give you access to a large number of calculator functions. Some menu keys, such as % h, display a single menu. Others, such as d, display multiple menus. Press " and $ to scroll and ... -
Page 9
d (key with multiple menus): MATH 1:4n/d³´Un/d 2: lcm( 3: gcd( 4: 4Pfactor 5: sum( 6: prod( NUM 1: abs( 2: round( 3: iPart( 4: fPart( 5: int( 6: min( 7: max( 8: mod( DMS 1: ¡ 2: ¢ 3: £ 4: r 5: g 6: ´DMS R ³´ P 1: P ´Rx( 2: P ´Ry( 3: R ´Pr( 4: R ´Pq( Scrolling expressions and history ... -
Page 10
... %b8< r Last answer %i The last entry performed on the home screen is stored to the variable ans. This variable is retained in memory, even after the calculator is turned off. To recall the value of ans: • Press % i (ans displays on the screen), or • Press any operations key (T, U, and so ... -
Page 11
3%c%i < Order of operations The TI-36X Pro calculator uses Equation Operating System (EOS™) to evaluate expressions...is evaluated from right to left. The expression 2^3^2 is evaluated as 2^(3^2), with a result of 512. The calculator evaluates expressions entered with F and a from left to right in ... -
Page 12
7th 8th 9th 10th 11th Permutations (nPr) and combinations (nCr). Multiplication, implied multiplication, division. Addition and subtraction. Conversions (n/d³´Un/d, F³´D, 4DMS). < completes all operations and closes all open parentheses. Examples +QPM 6 0 T 5 V M1 2 < ( M) 1TM8T12< % b 9 T... -
Page 13
... cursor. Clears variables x, y, z, t, a, b, c, and d to their default value of 0. Resets the calculator. Returns unit to default settings; clears memory variables, ...or denominator. Note: In Classic mode, only number entries are supported when using P. Fractions in Classic mode are shown with a double... -
Page 14
• P enters a simple fraction. Pressing P before or after a number can result in different behavior. Entering a number before pressing P makes that number the numerator. To enter fractions with operators or radicals, press P before you enter a number (in MathPrint™ mode only). • In MathPrintମ. -
Page 15
... n/ n d ³´U /d F³´D 4%@1$2" %˜< Examples P1.2 T 1.3 $ 4 < (MathPrint™ mode only) (MathPrint™ P M 5 T % b 5 mode only) F U 4 ( 1 ) ( 6 )$2(1)< Percentages %_ To perform a calculation involving a percentage, press % _ after entering the value of the percentage. Example 2 % _ V 150 < 15 -
Page 16
³ Problem A mining company extracts 5000 tons of ore with a concentration of metal of 3% and 7300 tons with a concentration of 2.3%. On the basis of ...of metal for a total value of 89012 dollars. EE key E E is a shortcut key to enter a number in scientific notation format. Example 2E5< q$"< -< 16 -
Page 17
Powers, roots and inverses F Calculates the square of a value. The TI-36X Pro calculator evaluates expressions entered with F and a ... and any odd integer root of a negative value. Gives the inverse of a value: 1/x. The calculator evaluates expressions entered with F and a from left to right in both ... -
Page 18
2%a< Pi g (multi-tap key) p = 3.141592653590 for calculations. p = 3.141592654 for display. Example p 2Vg< r ³ Problem What is the area of a circle if the radius is 12 cm? Reminder: A = p×r2 g V 12 F < r The area of the circle is 144... -
Page 19
Math d MATH d displays the MATH menu: 1:4n/d³´Un/d 2: lcm( 3: gcd( 4: 4Pfactor 5: sum( 6: prod( Examples n/ n d³´U /d Converts between simple fractions and mixed-number form. Least common multiple Greatest common divisor Prime factors Summation Product 9P2"d1< lcm( d2 6%`9)< d3 18 % ` 33 ) ... -
Page 20
Number functions d NUM d " displays the NUM menu: 1: abs( 2: round( 3: iPart( 4: fPart( 5: int( 6: min( 7: max( 8: mod( Examples abs( d"1 M%b5< d"2 1.245 % ` 1 5 < 4.9 L z < d "3 z ) < d "4 z ) V3< d "5 M 5.6 ) < d "6 4 % `M5 ) < d "7 .6 % ` .7 ) < Absolute value Rounded value Integer part of a ... -
Page 21
mod( d "8 17 % ` 12 6 < Angles d DMS d " " displays the DMS menu: 1: ¡ 2: ¢ 3: £ 4: r 5: g 6: ´DMS Specifies the angle unit modifier as degrees (º). Specifies the angle unit modifier as minutes ('). Specifies the angle unit modifier as seconds ("). Specifies a radian angle. Specifies a ... -
Page 22
DEG q< 2gd""4 < 4DMSS 1.5 d " " 6 < ³ Problem Two adjacent angles measure 12¡ 31¢ 45£ and 26... 39 degrees, 26 minutes and 23 seconds. ³ Problem It is known that 30¡ = p / 6 radians. In the default mode, degrees, find the sine of 30¡. Then set the calculator to radian mode and calculate the ... -
Page 23
Note: Press - to clear the screen between problems. - X 30 ) < q" -
Page 24
... X Y Z (multi-tap keys) Enter trigonometric functions (sin, cos, tan, sin-1, cos-1, tan-1), just as you would write them. Set the desired Angle mode before starting trigonometric calculations. Example Degree Mode tan q$$ -
Page 25
tan-1 Z Z1 ) < r cos 5VYgP4") < r ³ Problem Find angle A of the right triangle below. Then calculate angle B and the length of the hypotenuse c. Lengths are in meters. Round results to one decimal place. Reminder: 7 7⎞ - therefore m±A = tan-1 ⎛ -tan A = -⎝ 3 -
Page 26
... is 7.6 meters. Hyperbolics X Y Z (multi-tap keys) Pressing one of these multi-tap keys repeatedly lets you access the corresponding hyperbolic or inverse hyperbolic function. Angle modes do not affect hyperbolic calculations. Example Set floating q $ $ < decimal HYP XXX5)T2 < ## -
Page 27
...LN D5)V2< 10 › C CD D 2)< D DC C 5")< C .5 < e› Numeric derivative %A % A calculates an approximate derivative of expression with respect to variable, given the value at which to calculate the derivative and H (if not specified, the default is 1EM3). This function is... -
Page 28
...( once in expression. Because of the method used to calculate nDeriv(, the calculator can return a false derivative value at a nondifferentiable point. ³ Problem Find the slope of the tangent line to the curve f(x) = x3 - 4x at 2 x = ... -
Page 29
... x = -----3 minimum of the function must be at this point! Numeric integral %Q % Q calculates the numeric function integral of an expression with respect to a ... and an upper limit. Example in RAD angle mode % Q q " -
Page 30
< Notice that both areas are equal. Since this is a parabola with the vertex at (4,0) and zeros at (M2, 0) and (2, 0) you see that the symmetric areas are equal. Stored operations %m %n % n lets you store a sequence of operations. % m plays back the operation. To set an operation and then recall ... -
Page 31
... -1. %nV5U2< M5%m M1%m Memory and stored variables z L %h %{ The TI-36X Pro calculator has 8 memory variables-x, y, z, t, a, ... a real or complex number or an expression result to a memory variable. Features of the calculator that use variables (such as the solvers) will use the values that you store... -
Page 32
z is a multi-tap key that cycles through the variable names x, y, z, t, a, b, c, and d. You can also use z to recall the stored values for these variables. The name of the variable is inserted into the current entry, but the value assigned to the variable is used to evaluate the expression. To ... -
Page 33
Lzz < zz -
Page 34
... up to 42 items. Press % # to go to the top of a list, and % $ to go to the bottom of a list. List formulas accept all calculator functions and real numbers. Numeric notation, decimal notation, and angle modes affect the display of an element (except fractional elements). Example L1 v1P4$ 2P4$ 3P4$ ... -
Page 35
< v -
Page 36
... menu of statistical result variables. Use $ and # to locate the desired variable, and press < to select it. If you select this option before calculating 1-Var stats, 2-Var stats, or any of the regressions, a reminder appears. Analyzes statistical data from 1 data set with 1 measured variable, x. ... -
Page 37
3: 2-Var Stats 4: LinReg ax+b 5: QuadraticReg 6: CubicReg 7: LnReg a+blnx 8: PwrReg ax^b 9: ExpReg ab^x Analyzes paired data from 2 data sets with 2 measured variables-x, the independent variable, and y, the dependent variable. Frequency data may be included. Note: 2-Var Stats also computes ... -
Page 38
... x value. The defaults are mean mu=0 and standard deviation sigma=1. The probability density function ...and UPPERbnd for the specified mean mu and standard deviation sigma. The defaults are mu=0; sigma... specified by mean mu and standard deviation sigma. It calculates the x value associated with an area... -
Page 39
... data are stored in the StatVars menu until the next statistics or regression calculation. The results must be interpreted based on which type of statistics or regression ...n v or w Sx or Sy Definition Number of x or (x,y) data points. Mean of all x or y values. Sample standard deviation of x or y. 39 -
Page 40
...) Med Q3 (1-Var) MaxX Population standard deviation of x or y. Sum of all x or y values. Sum... y-intercept. Correlation coefficient. Uses a and b to calculate predicted x value when you input a y value... or parts that add up to 1. However, the sample standard deviation, Sx, is undefined for non-integer... -
Page 41
1-Var Example Find the mean of {45, 55, 55, 55} Clear all data Data vv$$$ < 45 $ 55 $ 55 $ 55 < %s %u 2 (Selects 1-Var Stats) $$ < Stat Stat Var 2< V2< 2-Var Example Data: (45,30); (55,25). Find: x¢(45) Clear all data Data vv$$$ < 45 $ 55 $ " 30 $ 25 $ 41 -
Page 42
Stat %u 3 (Selects 2-Var Stats) $$$ -
Page 43
... $ " 1 $ .5 $ 1 $ .5 < %u 2 (Selects 1-Var Stats) $""< < Anthony has an average (v) of 11.33 (to the nearest hundredth). On the calculator, n represents the total sum of the weights. n = 1 + 0.5 + 1 + 0.5. Gx represents the weighted sum of his scores. (12)(1) + (13)(0.5) + (10)(1) + (11)(0.5) = 34... -
Page 44
³ Problem The table below gives the results of a braking test. Test No. Speed (kph) Braking distance (m) 1 ... scatter plot of these data points suggest a linear relationship. The calculator uses the least squares method to find the line of best fit, y'=ax'+b, for data entered in lists. vv$$$ < 33 $ ... -
Page 45
...line of best fit, y'=0.67732519x'N18.66637321 models the linear trend of the data. Press... traveling at 55 kph. Regression example 1 Calculate an ax+b linear regression for the following data... all the result variables. Regression example 2 Calculate the exponential regression for the following data: 45... -
Page 46
... equation to f(x) in the I menu. Regression Equation Find the average value (y) of the data in L2 using StatVars. < %u 1 (Selects StatVars Notice that the title bar reminds you of your last statistical or regression calculation. Examine the I 2 table of values of the regression equation. 46 -
Page 47
..., the variables a and b (along with r and r2) will be calculated as a linear regression. Do not recalculate ... Stats after any other regression calculation if you want to preserve your... coefficients (a, b, c, d) and r values for your particular problem in the StatVars menu. Distribution example Compute... -
Page 48
< Probability H % -
Page 49
nPr 8HHH3< STO 4 rand 5L% -
Page 50
...value for the independent variable, x. The step can be positive or negative. The calculator automatically generates a series of values based on table start ... step. Lets you build a table manually by entering specific values for the independent variable, x. ³ Problem Find the vertex of the parabola,... -
Page 51
...smaller values to see points closer to (18, 324). ³ Problem A charity collected $3,600 to help ...funds run out. How many months will the charity support the kitchen? Reminder: If x = months and ... and press -
Page 52
...) % t NAMES % t displays the matrix NAMES menu, which shows the dimensions of the matrices and lets you use them in calculations. 1: [A] 2: [B] 3: [C] 4: [Ans] 5: [I2] 6: [I3] Definable matrix A Definable matrix B Definable matrix C Last matrix result (displayed as [Ans]=m×n) or last vector result ... -
Page 53
Matrix example Define matrix [A] as 1 2 3 4 Calculate the determinant, transpose, inverse, and rref of [A]. Define [A] % t ! < Set " -
Page 54
...) % ...NAMES % ...displays the vector NAMES menu, which shows the dimensions of the vectors and lets you use them in calculations. 1: [u] 2: [v] 3: [w] 4: [Ans] Definable vector u Definable vector v Definable vector w Last matrix result (displayed as [Ans]=m×n) or last vector result (displayed as [... -
Page 55
..., which lets you perform the following vector calculations: 1: DotProduct 2: CrossProduct 3: norm magnitude Syntax: DotP(... [w]. Vector example Define vector [u] = [ 0.5 8 ]. Define vector [v] = [ 2 3 ]. Calculate [u] + [v], DotP([u],[v]), and norm([v]). Define [u] % ...! < " -
Page 56
Add vectors %...< T %...$< < DotP 5 V 2 T 8 V 3 < Note: DotP is calculated here in two ways. norm r< % b 2 F T 3 F" r< Note: norm is calculated here in two ways. Solvers Numeric equation solver %‰ % ‰ prompts you for the equation and the values of the variables... -
Page 57
Example Reminder: If you have already defined variables, the solver will assume those values. Num-solv %‰ Left side 1 P2 " zF U5 z z z z z "" Right side 6 z U z z zz z z < Variable values 1P2$ 2P3$ 0.25 $ "" Solve for b < Note: Left-Right is the difference between the left- and right-hand ... -
Page 58
Example of quadratic equation Reminder: If you have already defined variables, the solver will assume those values. Poly-solv % -
Page 59
System of linear equations solver %‹ % ‹ solves systems of linear equations. You choose from 2×2 or 3×3 systems. Notes: • x, y, and z results are automatically stored in the x, y, and z variables. • Use r to toggle the results (x, y and z) as needed. • The 2x2 equation solver solves for... -
Page 60
Toggle r result type Example 3×3 system Solve: 5x - 2y + 3z = -9 4x + 3y + 5z = 4 2x + 4y - 2z = 14 System solve 3×3 system First equation Second equation Third equation Solutions %‹$ < 5< M2 < 3< M9< 4< 3< 5< 4< 2< 4< M2 < 14 < < $ $ 60 -
Page 61
... to binary (base 2). Converts to decimal (base 10). Converts to octal (base 8). Base type % - " displays the TYPE menu, which lets you designate the base of a number regardless of the calculator's current number-base mode. 1: h 2: b Designates a hexadecimal integer. Specifies a binary integer. 61 -
Page 62
3: d 4: o Specifies a decimal number. Specifies an octal integer. Examples in DEC mode Note: Mode can be set to DEC, BIN, OCT, or HEX. See the Mode section. d ´Hex 127 % - 1 1 %-2< 10000000 % - " 2 %-4< #< h ´Bin b ´Oct o ´Dec Boolean logic % - ! displays the LOGIC menu, which lets you ... -
Page 63
...: q $$$$ not, 2's "< %-!6 5 %i< DEC mode: q $$$$ < nand 192 % - ! 7 48 < Expression evaluation %‡ Press %‡ to input and calculate an expression using numbers, functions, and variables/parameters. Pressing %‡ from a populated home screen expression pastes the content to Expr=. If the user is ... -
Page 64
2zTzzz -
Page 65
Note: Displayed constant values are rounded. The values used for calculations are given in the following table. Constant speed of light c g...1.602176487×10M19 Coulombs atomic mass unit 1.660538782×10M27 kilograms standard 101325 Pascals atmosphere permittivity of 8.854187817620×10M12 Farads vacuum ... -
Page 66
Conversions The CONVERSIONS menu permits you to perform a total of 20 conversions (or 40 if converting both ways). To access the CONVERSIONS menu, press % -. Press one of the numbers (1-5) to select, or press # and $ to scroll through and select one of the CONVERSIONS submenus. The submenus include... -
Page 67
lb 4 kg kg 4 lb pounds to kilograms kilograms to pounds Temperature conversion Conversion ¡F 4 ¡C ¡C 4 ¡F ¡C 4 ¡K ¡K 4 ¡C Farenheit to Celsius Celsius to Farenheit Celsius to Kelvin Kelvin to Celsius Speed and length conversion Conversion km/hr 4 m/s m/s 4 km/hr LtYr 4 m m 4 LtYr pc 4 m... -
Page 68
Pressure conversion Conversion atm 4 kPa Pa 4 atm mmHg 4 kPa Pa 4 mmHg Examples Temperature (M22) atmospheres to Pascals Pascals to atmospheres millimeters of mercury to Pascals Pascals to millimeters of mercury %-2 -
Page 69
... %ˆ The calculator performs the following complex number calculations Addition, subtraction, multiplication, and division Argument and absolute ... Conjugate number calculations Setting the complex format: Set the calculator to DEC mode when computing with complex numbers. q $ $ $ Selects the REAL ... -
Page 70
Complex menu Description 1:± ± (polar angle character) Lets you paste the polar representation of a complex number (such as 5±p). 2 :polar angle angle( Returns the polar angle of a complex number. 3: magnitude abs( (or |þ| in MathPrint™ mode) Returns the magnitude (modulus) of a complex ... -
Page 71
4 r±q 3 T 4 ggg %ˆ4 < 5 %ˆ< 3gP2" % ˆ5 < 4 a+bi Conjugate: conj( % ˆ6 5 U 6 ggg ) < Real: real( % ˆ7 5 U 6 ggg) < Errors When the calculator detects an error, it returns an error message with the type of error. The following list includes some of the errors that you may encounter. To ... -
Page 72
... the COMPLEX error. DATA TYPE - You entered a value or variable that is the wrong data type. • For a function (including implied multiplication) or an instruction, you entered an argument that is an invalid data type, such as a complex number where a real number is required. • You attempted to ... -
Page 73
... coefficient cannot be zero - This error is displayed if a in a Polynomial solver calculation is prepopulated with zero, or if the you set a to zero and ...and n in the DISTR menus. INVALID EQUATION - This error is returned when: • The calculation contains too many pending operations (more than 23). ... -
Page 74
... - The Operation m is not defined. OVERFLOW - You attempted to enter, or you calculated a number that is beyond the range of the ... A singular matrix (determinant = 0) is not valid as the argument for -1. • The SinReg instruction or a polynomial regression generated a singular matrix (determinant = ... -
Page 75
... TOO COMPLEX - If you use too many levels of MathPrint™ complexity in a calculation, the TOO COMPLEX error is displayed (this error is not referring to complex numbers). LOW BATTERY - Replace the battery. Note: This message displays briefly and then disappears. Pressing - ... -
Page 76
...the National Capital Poison Center at 1-800-222-1222.) Battery disposal Do not mutilate, puncture, or ...burst or explode, releasing hazardous chemicals. Discard used batteries according to local regulations. How to remove or replace the battery The TI-36X Pro calculator uses one 3 volt CR2032 lithium ... -
Page 77
...hazardouswaste/perchlorate In case of difficulty Review instructions to be certain calculations were performed properly. Check the battery to ensure that it is fresh and properly installed. Change the battery when: • & does not turn the unit on, or • The screen goes blank, ... -
Page 78
Texas Instruments Support and Service For general information Home Page: education.ti.com KnowledgeBase and education.ti.com/support e-mail inquiries: Phone: International information: For technical support ...not toll-free): (972) 917-8324 (800) TI-CARES / (800) 842-2737 For U.S., Canada, ...