# Half Angle or Double Angle Examples

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Examples, solutions, videos, worksheets, games and activities to help PreCalculus students learn how to use the half angle or double angle formula in some examples.

The following diagrams show the half-angle identities and double-angle identities. Scroll down the page for more examples and solutions on how to use the half-angle identities and double-angle identities.

Half-Angle Identities
Example:
1. Determine the exact value of sin (π/8)
2. Determine the exact value of cos (105°)
3. Given cos A = -2/3 in quadrant II, determine cos(A/2), sin(A/2) and tan(A/2).

Double-Angle Identities
Example:
1. If sin A = 3/5 in quadrant II, find the exact value of cos(2A), sin(2A) and tan(2A). Then determine the quadrant of angle 2A.
2. Determine cos(A) given cos(2A) = -3/4 and terminates in quadrant III. Rewrite a Trigonometric Expression Using a Half Angle Identity
Example:
Rewrite the following trigonometric expression using a half angle identity.
1. (sin(5x))2
2. (cos(2x))4 Solve a Trigonometric Equation Using a Double Angle Identity
Example:
Solve on the interval [0,2π).
cos(2x) = cos(x)
How to solve a Trigonometric Equation Using a Double Angle Identity?
Example:
Solve on the interval [0,2π).
sin(2x) = 2cos2(x)

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