Texas Instruments TI-89 User Manual - Page 888

tanhê ( ) MATH/Hyperbolic menu tanhê (expression1) ⇒ expression tanhê (list1) ⇒ list tanhê (expression1) returns the inverse hyperbolic tangent of the argument as an expression. tanhê (list1) returns a list of the inverse hyperbolic tangents of each element of list1. In rectangular complex format mode: tanhê (0) ¸ 0 tanhê ({1,2.1,3}) ¸ {ˆ .518... ì 1.570...ø i ln(2) 2ì p2ø i} tanhê(squareMatrix1) ⇒ squareMatrix Returns the matrix inverse hyperbolic tangent of squareMatrix1. This is not the same as calculating the inverse hyperbolic tangent of each element. For information about the calculation method, refer to cos(). squareMatrix1 must be diagonalizable. The result always contains floating-point numbers. In Radian angle mode and Rectangular complex format mode: tanhê([1,5,3;4,2,1;6,ë2,1]) ¸ 5..100189...79ì......ì+2...170628453 iii .267...ì 1.490...øi .479...ì.947...øi ë.878...+1.790...øi ... ... ...  taylor( ) MATH/Calculus menu taylor(expression1, var, order[, point]) ⇒ expression Returns the requested Taylor polynomial. The polynomial includes non-zero terms of integer degrees from zero through order in (var minus point). taylor() returns itself if there is no truncated power series of this order, or if it would require negative or fractional exponents. Use substitution and/or temporary multiplication by a power of (var minus point) to determine more general power series. taylor(e^(‡(x)),x,2) ¸ taylor(e^(t),t,4)|t=‡(x) ¸ taylor(1/(xù (xì 1)),x,3) ¸ point defaults to zero and is the expansion point. expand(taylor(x/(xù(xì1)), x,4)/x,x) ¸ tCollect() MATH\Algebra\Trig menu tCollect(expression1) ⇒ expression Returns an expression in which products and integer powers of sines and cosines are converted to a linear combination of sines and cosines of multiple angles, angle sums, and angle differences. The transformation converts trigonometric polynomials into a linear combination of their harmonics. tCollect((cos(a))^2) ¸ cos(2ø a) + 1 2 tCollect(sin(a)cos(b)) ¸ sin(aì b)+sin(a+b) 2 Sometimes tCollect() will accomplish your goals when the default trigonometric simplification does not. tCollect() tends to reverse transformations done by tExpand(). Sometimes applying tExpand() to a result from tCollect(), or vice versa, in two separate steps simplifies an expression. 888 Appendix A: Functions and Instructions