Exact Value of Trig Functions Calculator
Use our calculator for the exact value of the trig functions to find the most common values of these functions for many angles!
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.