This is documentation for Mathematica 4, which was
based on an earlier version of the Wolfram Language.
Wolfram Research, Inc.

3.3.7 Trigonometric Expressions

Functions for manipulating trigonometric expressions.

This expands out a trigonometric expression.

In[1]:= TrigExpand[Sin[2 x] Cos[2 y]]

Out[1]=

This factors the expression.

In[2]:= TrigFactor[%]

Out[2]=

And this reduces the expression to a form linear in the trigonometric functions.

In[3]:= TrigReduce[%]

Out[3]=

TrigExpand works on hyperbolic as well as circular functions.

In[4]:= TrigExpand[Tanh[x + y]]

Out[4]=

TrigReduce reproduces the original form again.

In[5]:= TrigReduce[%]

Out[5]=

Mathematica automatically uses functions like Tan whenever it can.

In[6]:= Sin[x]^2/Cos[x]

Out[6]=

With TrigFactorList, however, you can see the parts of functions like Tan.

In[7]:= TrigFactorList[%]

Out[7]=

Converting to and from exponentials.

TrigToExp writes trigonometric functions in terms of exponentials.

In[8]:= TrigToExp[Tan[x]]

Out[8]=

ExpToTrig does the reverse, getting rid of explicit complex numbers whenever possible.

In[9]:= ExpToTrig[%]

Out[9]=

ExpToTrig deals with hyperbolic as well as circular functions.

In[10]:= ExpToTrig[Exp[x] - Exp[-x]]

Out[10]=

You can also use ExpToTrig on purely numerical expressions.

In[11]:= ExpToTrig[(-1)^(1/17)]

Out[11]=