# Solving Trigonometric Equations

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More Lessons for Trigonometry

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A series of free, online Trigonometry Video Lessons.
Videos, worksheets, and activities to help Trigonometry students.

In this lesson, we will learn

• how to solve trigonometric equations
• how to solve trigonometric equations by factoring

### Solving Trigonometric Equations

When solving trigonometric equations, we find all the angles that make the equation true. If there is no interval given, use periodicity to show the infinite number of solutions. Two ways to visualize the solutions are (1) the graph in the coordinate plane and (2) the unit circle. The unit circle is the more useful of the two in obtaining an answer.

Solving Trigonometric Equations
2 cos x = 1,
sin(2x) = cos x,
2 + cos 2x = 3 cos x,
sin x = tan x

Solving basic trig equations involving one trig function

### 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.

Solve trigonometric equations that are factorable or in quadratic form

This video solve a trigonometric equation in quadratic form by factoring.

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

Solving a Trigonometric Equation by Factoring
2 sin x cos x = cos x
cos x = cot x

Solving a Trigonometric Equation by Factoring
cos x = cot x

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