Texas Instruments TITANIUM TI-89 - Manual (Page 888)

888 Appendix A: Functions and Instructions
tanh ê ()
MATH/Hyperbolic menu
tanh ê ( expression1 )
⇒ ⇒ ⇒ ⇒ expression
tanh ê ( list1 ) ⇒ ⇒ ⇒ ⇒ list
tanh ê ( expression1 ) returns the inverse hyperbolic
tangent of the argument as an expression.
tanh ê ( 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 ... м 1.570 ...ш i
ln(2)
2 ì
p
2
ø i }
tanh ê( 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,л2,1]) ¸



 л .099…+.164…ш i .267…ì 1.490…шi …
л .087…м.725…ш i .479…ì.947…шi …
.511…м 2.083…ш i 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.
point defaults to zero and is the expansion point.
taylor( e ^(‡(x)),x,2) ¸
taylor( e ^(t),t,4)|t=‡(x) ¸
taylor(1/(xù (xì 1)),x,3) ¸
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.
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.
tCollect((cos(a))^2) ¸
cos(2ø a) + 1
2
tCollect(sin(a)cos(b)) ¸
sin(aì b)+sin(a+b)
2