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Double-angle identities

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Precalculus

13. CC.HSF.TF.C.9

13.2 Double-angle identities

Double-Angle Identities

Find the sine, cosine, or tangent of twice an angle using the double-angle formulas.

What You'll Learn

Double-angle identities come from the sum identities with both angles equal.

sin 2 theta equals 2 sin theta cos theta.

cos 2 theta has three equivalent forms using cos squared and sin squared theta.

tan 2 theta equals 2 tan theta over 1 minus tan squared theta.

Use whichever cosine form matches the information you already have.

What You'll Practice

Simplifying expressions using sin(2θ) = 2sin(θ)cos(θ)

Selecting among three cos(2θ) formulas to cancel terms

Proving trigonometric identities with double-angle formulas

Finding exact values of double-angle expressions from given ratios

Why This Matters

Double-angle identities are essential for simplifying complex trigonometric expressions in calculus, physics, and engineering. You'll use these formulas to solve equations, prove identities, and model periodic phenomena like waves and oscillations throughout higher math.

Before You Start — Make Sure You Can:

Use sine ratio to calculate angles and sides (Sin = \( \frac{o}{h}\) )Use cosine ratio to calculate angles and sides (Cos = \( \frac{a}{h}\) )Use tangent ratio to calculate angles and sides (Tan = \( \frac{o}{a}\) )Trigonometric ratios of angles in radians

This Unit Includes

10 Video lessons

Practice exercises

Learning resources

Skills

Double-Angle Identities

Trigonometric Identities

Simplification

Factoring

Quotient Identities

Reference Angles

Proof Techniques

IL Curriculum Aligned