Texas Instruments PLUS TI-89 - Manual (Page 529)

512 Appendix A: Functions and Instructions
8992APPA.DOC TI-89 / TI-92 Plus: Appendix A (US English) Susan Gullord Revised: 02/23/01 1:48 PM Printed: 02/23/01 2:21 PM Page 512 of 132
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:
tanhк([1,5,3;4,2,1;6,л 2,1])
¸





 л.099…+.164…шi .267…м 1.490…шi …
л.087…м.725…шi .479…м.947…шi …
.511…м 2.083…шi л.878…+1.790…шi …
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