Cos() – Texas Instruments TITANIUM TI-89 User 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…