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ExpToTrig[expr]

converts exponentials in expr to trigonometric functions.

Details
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Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
See Also
Tech Notes
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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  (3)

ExpToTrig is the inverse of TrigToExp:

ExpToTrig threads element‐wise 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_2025_exptotrig, author="Wolfram Research", title="{ExpToTrig}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/ExpToTrig.html}", note=[Accessed: 11-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_exptotrig, organization={Wolfram Research}, title={ExpToTrig}, year={2007}, url={https://reference.wolfram.com/language/ref/ExpToTrig.html}, note=[Accessed: 11-August-2025]}