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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]=