Trigonometry Identities

Half Angle Formulas

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.

Sign from quadrant of θ/2
Two forms for tan(θ/2)
Unit circle — θ and θ/2
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Angle θ (degrees)
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Results
Enter θ and press Compute.
θ / 2
cos θ
sin θ
sin(θ/2)
Form 1: sin θ / (1+cos θ)
Form 2: (1−cos θ) / sin θ
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Unit Circle — θ and θ/2
Half Angle Identities
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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