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TrigToExp—Wolfram Documentation

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TrigToExp[expr]

converts trigonometric functions in expr to exponentials.

Details
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Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
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TrigToExp

TrigToExp[expr]

converts trigonometric functions in expr to exponentials.

Details

  • TrigToExp operates on both circular and hyperbolic functions, and their inverses.
  • TrigToExp automatically threads over lists, as well as equations, inequalities, and logic functions.

Examples

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Basic Examples  (2)

Convert from trigonometric functions to complex exponentials:

Wolfram Language code: TrigToExp[Cos[x]]

Convert from hyperbolic functions to exponentials:

Wolfram Language code: TrigToExp[Sinh[x]]

Scope  (5)

Convert from trigonometric functions to exponentials:

Wolfram Language code: TrigToExp[Cos[x] + I Sin[x]]

Convert from hyperbolic functions to exponentials:

Wolfram Language code: TrigToExp[Tanh[x]]

Convert from inverse trigonometric functions to logarithms:

Wolfram Language code: TrigToExp[ArcSin[x]]

Convert from inverse hyperbolic functions to logarithms:

Wolfram Language code: TrigToExp[ArcCoth[x]]

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

Wolfram Language code: TrigToExp[{Sin[x], Cos[x], Tan[x]}]
Wolfram Language code: TrigToExp[Sinh[x] ≤ 11 && ArcTan[x] == 7]

Applications  (2)

Rewrite compositions of trigonometric and inverse trigonometric functions:

Wolfram Language code: TrigToExp[Sin[5 ArcSin[x]]]
Wolfram Language code: FullSimplify[%]

Check:

Wolfram Language code: TrigReduce[% /. x -> Sin[θ]]

Find the exponential form of solutions to differential equations:

Wolfram Language code: DSolve[{y''[t] + ω^2y[t] == 0, y[0] == 1, y'[0] == I ω}, y[t], t]
Wolfram Language code: TrigToExp[%]

Properties & Relations  (2)

TrigToExp threads element‐wise over lists, equations, inequalities and logic functions:

Wolfram Language code: TrigToExp[Sin[x] < x < Tan[x]]
Wolfram Language code: TrigToExp[Sin[x] == Pi / 3]

TrigToExp is an inverse of ExpToTrig:

Wolfram Language code: {ExpToTrig[Exp[I x]], ExpToTrig[Log[z + Sqrt[z^2 + 1]]]}
Wolfram Language code: TrigToExp[%]
Wolfram Research (1996), TrigToExp, Wolfram Language function, https://reference.wolfram.com/language/ref/TrigToExp.html (updated 2007).

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_trigtoexp, author="Wolfram Research", title="{TrigToExp}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/TrigToExp.html}", note=[Accessed: 14-November-2026]}

BibLaTeX

@online{reference.wolfram_2026_trigtoexp, organization={Wolfram Research}, title={TrigToExp}, year={2007}, url={https://reference.wolfram.com/language/ref/TrigToExp.html}, note=[Accessed: 14-November-2026]}