Half Angle or Double Angle Examples

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).
   

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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.

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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

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Solve a Trigonometric Equation Using a Double Angle Identity
Example:
Solve on the interval [0,2π).
cos(2x) = cos(x)

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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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