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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]= 
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