# 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:
 In:= Out= This factors the expression:
 In:= Out= And this reduces the expression to a form that is linear in the trigonometric functions:
 In:= Out= TrigExpand works on hyperbolic as well as circular functions:
 In:= Out= TrigReduce reproduces the original form again:
 In:= Out= The Wolfram System automatically uses functions like Tan whenever it can:
 In:= Out= With TrigFactorList, however, you can see the parts of functions like Tan:
 In:= Out= 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:
 In:= Out= TrigToExp also works with hyperbolic functions:
 In:= Out= ExpToTrig does the reverse, getting rid of explicit complex numbers whenever possible:
 In:= Out= ExpToTrig deals with hyperbolic as well as circular functions:
 In:= Out= You can also use ExpToTrig on purely numerical expressions:
 In:= Out= 