Half Angle

Half angle formula: sin(θ/2) = ±√((1 − cos θ)/2)

sinθ2=±1cosθ2\sin\tfrac{\theta}{2} = \pm\sqrt{\dfrac{1 - \cos\theta}{2}}

sin(θ/2) = ±√((1 − cos θ)/2), obtained by rearranging cos 2θ = 1 − 2sin²θ. The ± is not optional: you choose the sign from the quadrant θ/2 lands in, not from the sign of θ. Forgetting to check that quadrant is the classic way to lose the mark.

Related Half Angle identities

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Half Angle questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.