# ExpToTrig

ExpToTrig[expr]

converts exponentials in expr to trigonometric functions.

# Details • ExpToTrig generates both circular and hyperbolic functions.
• ExpToTrig tries when possible to give results that do not involve explicit complex numbers.
• ExpToTrig automatically threads over lists, as well as equations, inequalities and logic functions.

# Examples

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## Basic Examples(2)

Convert from exponentials to trigonometric functions:

Convert from exponentials to hyperbolic functions:

## Scope(6)

Convert from exponentials to trigonometric functions:

Convert from exponentials to hyperbolic functions:

Convert from logarithms to inverse trigonometric functions:

Convert from logarithms to inverse hyperbolic functions:

ExpToTrig converts rational powers of to the equivalent trigonometric expressions:

ExpToTrig threads elementwise over lists, equations, inequalities and Boolean operators:

## Applications(2)

Show that the unit circle maps to an interval in the Joukowski map:

Find the hyperbolic forms of solutions to differential equations:

## Properties & Relations(2)

ExpToTrig is the inverse of TrigToExp:

ExpToTrig threads elementwise over lists, equations, inequalities and logic functions: