# TrigFactor

TrigFactor[expr]

factors trigonometric functions in expr.

# Details

• TrigFactor operates on both circular and hyperbolic functions.
• TrigFactor splits up sums and integer multiples that appear in arguments of trigonometric functions, and then factors resulting polynomials in trigonometric functions, using trigonometric identities when possible.
• TrigFactor automatically threads over lists, as well as equations, inequalities, and logic functions.

# Examples

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## Basic Examples(3)

Factor a trigonometric expression into a product of terms:

Factor a hyperbolic trigonometric expression:

Factor trigonometric expressions of several variables:

## Scope(6)

Factor a univariate trigonometric expression:

Factor a multivariate trigonometric expression:

Factor a hyperbolic trigonometric expression:

Factor a rational combination of trigonometric functions:

TrigFactor threads over equations and inequalities:

## Applications(2)

Solve a trigonometric polynomial equation:

Reduce it to elementary trigonometric equations:

Detect common roots of trigonometric polynomials:

Common roots of and are the roots of :

Using the original polynomials yields a more complicated result:

To show that the root sets are equal, it suffices to check within one period:

## Properties & Relations(2)

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

TrigFactor threads elementwise over lists, inequalities, equations, and logical operations:

## Possible Issues(1)

A trigonometric expression can be factored in many different ways:

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_trigfactor, author="Wolfram Research", title="{TrigFactor}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/TrigFactor.html}", note=[Accessed: 18-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_trigfactor, organization={Wolfram Research}, title={TrigFactor}, year={2007}, url={https://reference.wolfram.com/language/ref/TrigFactor.html}, note=[Accessed: 18-July-2024 ]}