# 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.
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This factors the expression.
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And this reduces the expression to a form that is linear in the trigonometric functions.
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TrigExpand works on hyperbolic as well as circular functions.
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TrigReduce reproduces the original form again.
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The Wolfram System automatically uses functions like Tan whenever it can.
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With TrigFactorList, however, you can see the parts of functions like Tan.
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 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.
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TrigToExp also works with hyperbolic functions.
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ExpToTrig does the reverse, getting rid of explicit complex numbers whenever possible.
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ExpToTrig deals with hyperbolic as well as circular functions.
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You can also use ExpToTrig on purely numerical expressions.
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