Half Angle Calculator

Half Angle Calculator

Calculate half-angle trigonometric values.

Last updated: June 2026 | By Patchworkr Team

Input Angle

sin(θ/2)
0.500000
cos(θ/2)
0.866025
tan(θ/2)
0.577350

Why it matters

Half-angle identities let you express trig values for θ/2 using information about θ.

Key identities

sin(θ/2) = ±sqrt((1 - cos θ)/2), cos(θ/2) = ±sqrt((1 + cos θ)/2).

Worked Example

Use θ = 90°.

1. Half angle = 45°

2. sin(45°) ≈ 0.7071

3. cos(45°) ≈ 0.7071

Final answer: sin, cos about 0.7071, tan = 1

Frequently Asked Questions

Do I enter θ or θ/2?

Enter the full angle θ and the tool calculates the half angle.

Can I use radians?

Yes, switch the unit to radians.

Why is tan(θ/2) sometimes huge?

It grows near angles where cos(θ/2) is close to zero.

Are results exact?

No, they are numerical approximations.

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