# Factoring Trigonometric Equations

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Examples, solutions, videos, worksheets, and activities to help PreCalculus students learn how to factor trigonometric equations.

The following diagram shows how to factor and solve trigonometric equations. Scroll down the page for more examples and solutions.

Factoring Trigonometric Equations
Solving second degree trig functions can be accomplished by factoring polynomials into products of binomials. When factoring trigonometric equations, we can use the zero product property to set up two first degree trig equations that you can solve using the unit circle. If an equation has sine and cosine, we substitute for one with an identity.
This video solve a trigonometric equation by factoring.
cos2 x − cos x − 2 = 0

Solving a trig equation that requires substitution and factoring.
It reviews how to solve a trig equation using the unit circle to determine trig function values.
2cos2 x − sin x = 1

Solving a Trigonometric Equation by Factoring, Example 1
2sin2 x = 1 + cos x

Solving a Trigonometric Equation by Factoring, Example 2
2sin x cos x = cos x

Solving a Trigonometric Equation by Factoring, Example 3
cos x = cot x

Solving trig equations that are factorable or in quadratic form.
tan2 x − 1 = 0
2 sin2 x = −3sin x − 1

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