More Lessons for PreCalculus

Math Worksheets

Videos, worksheets, games and activities to help PreCalculus students learn how to derive and use the half angle identities.

Using Half-Angle Identities to Solve a Trigonometric Equation

Half Angle Identities to Evaluate Trigonometric Expressions, Example 1.

This video gives some half angle identities and show how they can be used to solve some trigonometric equations.

This video gives some half angle identities and show how they can be used to solve some trigonometric equations.

This video gives some half angle identities and show how they can be used to solve some trigonometric equations.

The derivations of the half-angle identities for both sine and cosine, plus listing the tangent ones. Then a couple of examples using the identities.

The Half-Angle Identities : 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(2alpha) becomes cos(theta) 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.

How to use the power reduction formulas to derive the half-angle formulas.

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