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Advanced Topic: Polynomials over Algebraic Number FieldsExpressions Involving Complex Variables

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]=

Advanced Topic: Polynomials over Algebraic Number FieldsExpressions Involving Complex Variables