Double-angle formulas

Math

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

  • sin(60°) = 2sin(30°)cos(30°) = 2(1/2)(√3/2) = √3/2
  • Simplifying sin(2x)cos(x) in an integral
  • 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

Half-angle formulas Sum and difference formulas Verifying identities Pythagorean identities

Study This Concept

Practice double-angle formulas with free review games in these units:

Pre-Calculus Unit 5: Analytic Trigonometry Trigonometry Unit 5: Trigonometric Identities