Math
Half-angle formulas.
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
Real-world.
- 1 Finding sin(15°) using the half-angle formula with 30°
- 2 Calculating cos(π/8) from cos(π/4)
- 3 Evaluating tan(22.5°) exactly
Key Fact
sin(θ/2) = ±√((1 − cosθ)/2), cos(θ/2) = ±√((1 + cosθ)/2)