# TrigExpand

TrigExpand[expr]

expands out trigonometric functions in expr.

# Details

• TrigExpand operates on both circular and hyperbolic functions.
• TrigExpand splits up sums and integer multiples that appear in arguments of trigonometric functions, and then expands out products of trigonometric functions into sums of powers, using trigonometric identities when possible.
• TrigExpand automatically threads over lists, as well as equations, inequalities, and logic functions.

# Examples

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## Basic Examples(2)

Expand trigonometric expressions:

Expand hyperbolic trigonometric expressions:

## Scope(4)

Expand trigonometric expressions:

Expand hyperbolic trigonometric expressions:

TrigExpand threads over equations and inequalities:

## Applications(1)

Because of the multivaluedness of ArcSin this law does not hold everywhere:

## Properties & Relations(3)

TrigExpand and TrigReduce are, generically, inverses of each other:

The expressions are identical modulo trigonometric Pythagorean identities:

Compare TrigExpand, TrigFactor, and TrigReduce on the same expression:

Use TrigExpand to construct a ChebyshevT polynomial:

## Possible Issues(1)

Expand trigonometric functions using half-angles:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_trigexpand, author="Wolfram Research", title="{TrigExpand}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/TrigExpand.html}", note=[Accessed: 10-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_trigexpand, organization={Wolfram Research}, title={TrigExpand}, year={2007}, url={https://reference.wolfram.com/language/ref/TrigExpand.html}, note=[Accessed: 10-September-2024 ]}