Cos() – Texas Instruments PLUS TI-89 User Manual
Page 440
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:
2 X
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
ó or ô to 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 (
l
i
) and
eigenvectors (V
i
) of A.
squareMatrix1
must be diagonalizable.
Also, it cannot have symbolic variables
that have not been assigned a value.
2. Form the matrices:
B =
l
1
0
… 0
0
l
2
… 0
0
0
… 0
0
0
…
l
n
and X = [V
1
,V
2
, … ,V
n
]
3. Then A = X B Xê and f(A) = X f(B) Xê. For
example, cos(A) = X cos(B) Xê where:
cos (B) =
cos(
)
cos(
)
cos(
)
λ
λ
λ
1
2
0
0
0
0
0
0
0
0
0
K
K
K
K
n
All computations are performed using
floating-point arithmetic.
In Radian angle mode:
cos([1,5,3;4,2,1;6,л 2,1]) ¸
.212… .205… .121…
.160… .259… .037…
.248… л.090… .218…