Half-angle formulas

Math

Definition

Trigonometric identities that express the sine, cosine, or tangent of half an angle in terms of the full angle. They are derived from double-angle formulas and are useful for finding exact values of trig functions.

Examples

  • Finding sin(15°) using the half-angle formula with 30°
  • Calculating cos(π/8) from cos(π/4)
  • Evaluating tan(22.5°) exactly
Key Fact

sin(θ/2) = ±√((1 − cosθ)/2), cos(θ/2) = ±√((1 + cosθ)/2)

Related Terms

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

Study This Concept

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

Trigonometry Unit 5: Trigonometric Identities