## 3.3.7 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[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]=

 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[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]=

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