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Half Angle Formula Calculator

Calculate sin(θ/2), cos(θ/2), and tan(θ/2) using the half angle formulas.

Calculator

Unit

DegreesRadians

Angle θ (°)

Quadrant of θ/2 (for sign)

sin(θ/2) = ±√((1 - cos θ)/2)

cos(θ/2) = ±√((1 + cos θ)/2)

tan(θ/2) = (1 - cos θ)/sin θ

= sin θ/(1 + cos θ)

Note: The ± sign depends on which quadrant θ/2 falls in. Use the quadrant selector to determine the correct sign.

Determine which quadrant θ/2 is in. Sin is positive in Q1 and Q2. Cos is positive in Q1 and Q4. Choose accordingly.

When you need exact values (like sin 15° = sin(30°/2)), in integration, and when simplifying trig expressions.

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