Half Angle Calculator
The half-angle calculator is here to help you with computing the values of trigonometric functions for an angle and the angle halved.
sin 2θ0.984807753θ = 40°, so 2θ = 80°
cos 2θ0.1736481777
sin(θ/2)0.3420201433
cos(θ/2)0.9396926208
sin²θ + cos²θ1always exactly 1
Cofunction: sin θ = cos(90° − θ)0.6427876097
Identities at this angle
| Identity | Value |
|---|---|
| sin 2θ = 2 sin θ cos θ | 0.984807753 |
| cos 2θ = cos²θ − sin²θ | 0.1736481777 |
| tan 2θ = 2 tan θ ÷ (1 − tan²θ) | 5.6712818196 |
| sin(θ/2) = ±√((1 − cos θ)/2) | 0.3420201433 |
| cos(θ/2) = ±√((1 + cos θ)/2) | 0.9396926208 |
| sin²θ = (1 − cos 2θ)/2 | 0.4131759112 |
| cos²θ = (1 + cos 2θ)/2 | 0.5868240888 |
The formula
double angle, half angle and power reducing, all at once
Why these matter
The Pythagorean identity sin²θ + cos²θ = 1 is the one everything else rests on. Double-angle formulas let you express a function of 2θ in terms of θ; power-reducing formulas run the other way, trading a squared function for a plain one at double the angle — which is precisely what makes integrals like ∫sin²x dx tractable.
Note the ± on the half-angle formulas: the sign depends on which quadrant θ/2 lands in, so the calculator shows the positive root.