Appendix A: Functions and Instructions 795
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) =
1
2
cos( ) 0 0
0cos() 0
00 0
00 cos()
n
λ
λ
λ
…
…
…
…
All computations are performed using floating-
point arithmetic.
In Radian angle mode:
cos([1,5,3;4,2,1;6,ë 2,1]) ¸
.212… .205… .121…
.160… .259… .037…
.248… ë.090… .218…
cosê () 2Rkey
cosê (
expression1
) ⇒
⇒⇒
⇒
expression
cosê (
list1
) ⇒
⇒⇒
⇒
list
cosê (
expression1
) returns the angle whose cosine
is
expression1
as an expression.
cosê (
list1
) returns a list of the inverse cosines of
each element of
list1
.
Note: The result is returned as a degree, gradian
or radian angle, according to the current angle
mode setting.
In Degree angle mode:
cosê (1) ¸ 0
In Gradian angle mode:
cosê (0) ¸ 100
In Radian angle mode:
cosê ({0,.2,.5}) ¸
{
p
2
1.369... 1.047...}
cosê(
squareMatrix1
) ⇒
⇒⇒
⇒
squareMatrix
Returns the matrix inverse cosine of
squareMatrix1
.
This is
not
the same as calculating the inverse
cosine 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:
cosê([1,5,3;4,2,1;6,ë 2,1])
¸
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