# 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

open allclose all

## 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(3)

ExpToTrig is the inverse of TrigToExp:

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

Wolfram Research (1996), ExpToTrig, Wolfram Language function, https://reference.wolfram.com/language/ref/ExpToTrig.html (updated 2007).

#### Text

Wolfram Research (1996), ExpToTrig, Wolfram Language function, https://reference.wolfram.com/language/ref/ExpToTrig.html (updated 2007).

#### CMS

Wolfram Language. 1996. "ExpToTrig." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2007. https://reference.wolfram.com/language/ref/ExpToTrig.html.

#### APA

Wolfram Language. (1996). ExpToTrig. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ExpToTrig.html

#### BibTeX

@misc{reference.wolfram_2024_exptotrig, author="Wolfram Research", title="{ExpToTrig}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ExpToTrig.html}", note=[Accessed: 09-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_exptotrig, organization={Wolfram Research}, title={ExpToTrig}, year={2007}, url={https://reference.wolfram.com/language/ref/ExpToTrig.html}, note=[Accessed: 09-August-2024 ]}