The Half-Angle Identities - Concept

Concept Concept (1)

The half angle identities come from the power reduction formulas using the key substitution alpha=theta/2 twice, once on the left and right sides of the equation. With half angle identies, on the left side, this yields (after a square root) cos(theta/2) or sin(theta/2); on the right side cos(2theta) becomes cos( ) because 2(1/2)=1. For a problem like sin(pi/12), remember that theta/2=pi/12, or theta=pi/6, when substituting into the identity.

Sample Sample Problems (3)

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The Half-Angle Identities - Problem 1
Problem 1
How to use a half-angle formula to evaluate sin(pi/8).
The Half-Angle Identities - Problem 2
Problem 2
How to use a half-angle formula to evaluate cos(105).
The Half-Angle Identities - Problem 3
Problem 3
How to use the double-angle formulas for sine and cosine to derive a half-angle formula for tangent.
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