How to derive it
- Write 15° = 45° − 30°.
- cos(A − B) = cos A cos B + sin A sin B.
- = (1/√2)(√3/2) + (1/√2)(1/2) = (√3 + 1)/(2√2).
- Multiply top and bottom by √2: (√6 + √2)/4.
All trig ratios of 15°
| Ratio | Exact | Decimal |
|---|---|---|
| sin 15° | (√6 − √2)/4 | 0.2588 |
| cos 15° | (√6 + √2)/4 | 0.9659 |
| tan 15° | 2 − √3 | 0.2679 |
| cosec 15° | 1 ÷ sin 15° | 3.8637 |
| sec 15° | 1 ÷ cos 15° | 1.0353 |
| cot 15° | 1 ÷ tan 15° | 3.7321 |
Exact values of special angles
For whole-degree values from 0° to 90°, see the trigonometry table.
Questions students ask
What is the value of cos 15°?
(√6 + √2)/4, which is about 0.9659.
What is cos 15° in radians?
15° is π/12 radians, so cos(π/12) = (√6 + √2)/4.
Is cos 15° equal to sin 75°?
Yes. cos θ = sin(90° − θ), so cos 15° = sin 75°.
How do you find cos 15° without a calculator?
Write 15° = 45° − 30°. cos(A − B) = cos A cos B + sin A sin B. = (1/√2)(√3/2) + (1/√2)(1/2) = (√3 + 1)/(2√2). Multiply top and bottom by √2: (√6 + √2)/4.