Half angle formula: sin(θ/2) = ±√((1 − cos θ)/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
Common questions
What is the sin θ/2 identity?
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.
When do you use the sin θ/2 identity?
Forgetting to check that quadrant is the classic way to lose the mark.
Which identities are related to sin θ/2?
sin θ/2 belongs to the Half Angle group. The identities used alongside it most often are cos θ/2 and tan θ/2.
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.