This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
 Mathematica Tutorial Functions »|Tutorials »

# Trigonometric Expressions

 TrigExpand[expr] expand trigonometric expressions out into a sum of terms TrigFactor[expr] factor trigonometric expressions into products of terms TrigFactorList[expr] give terms and their exponents in a list TrigReduce[expr] reduce trigonometric expressions using multiple angles

Functions for manipulating trigonometric expressions.

This expands out a trigonometric expression.
 Out[1]=
This factors the expression.
 Out[2]=
And this reduces the expression to a form linear in the trigonometric functions.
 Out[3]=
TrigExpand works on hyperbolic as well as circular functions.
 Out[4]=
TrigReduce reproduces the original form again.
 Out[5]=
Mathematica automatically uses functions like Tan whenever it can.
 Out[6]=
With TrigFactorList, however, you can see the parts of functions like Tan.
 Out[7]=
 TrigToExp[expr] write trigonometric functions in terms of exponentials ExpToTrig[expr] write exponentials in terms of trigonometric functions

Converting to and from exponentials.

TrigToExp writes trigonometric functions in terms of exponentials.
 Out[8]=
TrigToExp also works with hyperbolic functions.
 Out[9]=
ExpToTrig does the reverse, getting rid of explicit complex numbers whenever possible.
 Out[10]=
ExpToTrig deals with hyperbolic as well as circular functions.
 Out[11]=
You can also use ExpToTrig on purely numerical expressions.
 Out[12]=