Compute sin(θ/2), cos(θ/2), and tan(θ/2) using the half-angle identities. The sign is determined by the quadrant of θ/2, and both tan forms are shown.
sin(θ/2) = ±√((1 − cos θ)/2)
cos(θ/2) = ±√((1 + cos θ)/2)
tan(θ/2) = sin θ/(1 + cos θ) = (1 − cos θ)/sin θ
The ± sign for sin(θ/2) and cos(θ/2) depends on the quadrant of θ/2 (not θ). The tan(θ/2) formulas are sign-free — they automatically give the correct sign regardless of quadrant.
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