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
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])
¸
ë.099…+.164…øi .267…ì1.490…øi …
ë.087…ì.725…øi .479…ì.947…øi …
.511…ì2.083…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.
point defaults to zero and is the expansion
point.
taylor(e^(‡(x)),x,2) ¸
taylor(e^(t),t,4)|t=‡(x) ¸
taylor(1/(xù(xì1)),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(2øa) + 1
2
tCollect(sin(a)cos(b)) ¸
sin(aìb)+sin(a+b)
2