Appendix A: Functions and Instructions 423
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 423 of 132
cos() TI-89: 2X key TI-92 Plus: X key
cos(expression1) ⇒ expression
cos(list1) ⇒ list
cos(expression1) returns the cosine of the
argument as an expression.
cos(list1) returns a list of the cosines of all
elements in list1.
Note: The argument is interpreted as either a
degree or radian angle, according to the
current angle mode setting. You can use
óor ôto override the angle mode
temporarily.
In Degree angle mode:
cos((p/4)ô) ¸
‡
2
2
cos(45) ¸‡2
2
cos({0,60,90}) ¸{1 1/2 0}
In Radian angle mode:
cos(p/4) ¸
‡
2
2
cos(45¡) ¸‡2
2
cos(squareMatrix1) ⇒ squareMatrix
Returns the matrix cosine of squareMatrix1.
This is not the same as calculating the cosine
of each element.
When a scalar function f(A) operates on
squareMatrix1 (A), the result is calculated by
the algorithm:
1. Compute the eigenvalues (li) and
eigenvectors (Vi) of A.
squareMatrix1 must be diagonalizable.
Also, it cannot have symbolic variables
that have not been assigned a value.
2. Form the matrices:
B =
l1 0 … 0
0 l2 … 0
0 0 … 0
0 0 … ln
and X = [V1,V2, … ,Vn]
3. Then A = X B Xêand f(A) = X f(B) Xê. For
example, cos(A) = X cos(B) Xêwhere:
cos (B) =
cos( )
cos( )
cos( )
λ
λ
λ
1
2
00
00
00 0
00
K
K
K
Kn
All computations are performed using
floating-point arithmetic.
In Radian angle mode:
cos([1,5,3;4,2,1;6,ë2,1]) ¸
.212… .205… .121…
.160… .259… .037…
.248… ë.090… .218…