This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.

 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]=