Calculate half-angle trigonometric values.
Last updated: June 2026 | By Patchworkr Team
Half-angle identities let you express trig values for θ/2 using information about θ.
sin(θ/2) = ±sqrt((1 - cos θ)/2), cos(θ/2) = ±sqrt((1 + cos θ)/2).
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
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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