Math

Double-angle formulas.

Definition

Double-angle formulas express trigonometric functions of 2θ in terms of functions of θ. They are derived from the sum formulas by setting both angles equal to θ.

Examples

Real-world.

  • 1 sin(60°) = 2sin(30°)cos(30°) = 2(1/2)(√3/2) = √3/2
  • 2 Simplifying sin(2x)cos(x) in an integral
  • 3 Finding exact values like cos(π/6) using cos(2·π/12)
Key Fact

sin(2θ) = 2sinθcosθ; cos(2θ) = cos²θ - sin²θ = 2cos²θ - 1 = 1 - 2sin²θ

Related terms

Tangled up with.

Half-angle formulas → Sum and difference formulas → Verifying identities → Pythagorean identities →
Studied in

2 units use this concept.

Pre-Calculus Analytic Trigonometry → Trigonometry Trigonometric Identities →