Texas Instruments TITANIUM TI-89 - Manual (Page 795)

Appendix A: Functions and Instructions 795
cos() 2 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 a degree,
gradian or radian angle, according to the current
angle mode setting. You can use ó ,
G o r 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 Gradian angle mode:
cos({0,50,100}) ¸ {1
‡ 2
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 =







 l1 0 … 0
0 l2 … 0
0 0 … 0
0 0 … ln
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( 0 0
0 0 0
0 ) cos( 0
0 0 ) cos(
2
1
n
λ
λ
λ
…
…
…
…
All computations are performed using floating-
point arithmetic.
In Radian angle mode:
cos([1,5,3;4,2,1;6,л2,1]) ¸





 .212… .205… .121…
.160… .259… .037…
.248… л.090… .218…