Description:
Linearizes and simplifies trigonometric expressions. Note that this function does not collect
sin and cos terms of the same angle.
P
Access:
TRIG
Input:
An expression.
Output:
The transformation of the expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Example:
Linearize and simplify the following:
cos
x
Command:
TLIN(COS(X)^4)
Result:
(1/8)*COS(4X)+(1/2)*COS(2X)+(3/8)
See also:
SIMPLIFY, TCOLLECT, TEXPAND
TRIG
Type:
Command
Description:
Converts complex logarithmic and exponential subexpressions into their equivalent
trigonometric expressions. It also simplifies trigonometric expressions by using:
2
sin
x
+
P
Access:
TRIG
Input:
A complex expression with logarithmic and/or exponential terms, or a trigonometric
expression.
Output:
The transformed expression.
Flags:
Exact mode must be set (flag –105 clear).
Numeric mode must not be set (flag -3 clear).
Radians mode must be set (flag –17 set).
Prefers cosine terms if "prefer cos" is selected (flag –116 clear), prefers sine terms if flag –116
is set.
Must be in Complex mode (flag –103 set) if a complex expression is being simplified.
Example:
Express the following in trigonometric terms:
ln
x i
+
Command:
TRIG(LN(X+i))
2
L N X
+
- - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ----------------- -
Result:
See also:
TRIGCOS, TRIGSIN, TRIGTAN
TRIGCOS
Type:
Command
Description:
Simplifies a trigonometric expression by applying the identity:
sin
x
Returns only cosine terms if possible.
Trigonometry, ...ÑLL
Access:
Input:
An expression with trigonometric terms.
, Trigonometry, ...ÑL
4
2
cos
x
=
1
, Trigonometry, ...ÑLL
⎛ ⎞
1
2 i A T AN
1
+
-- - ⎝ ⎠
x
2
2
2
+
cos
x
=
1
Computer Algebra Commands 4-75