Work out half angle formula instantly with clear inputs, formula shown and shareable results.
Rearranging cos 2x = 1 − 2sin²x gives the half-angle formulas sin(θ/2) = ±√((1 − cos θ)/2) and cos(θ/2) = ±√((1 + cos θ)/2), with the sign fixed by the quadrant of θ/2.
Sine
sin(θ/2) = ±√((1 − cos θ) / 2)
Cosine
cos(θ/2) = ±√((1 + cos θ) / 2)
Tangent
tan(θ/2) = sin θ / (1 + cos θ)
sin 30° = 0.5 and cos 30° = 0.8660254, and the radical form √((1 − 0.5)/2) = 0.5 agrees.
Look at which quadrant θ/2 lands in; the radical only gives the magnitude.