Sin 15 Degrees

Sin, Cos, Tan, Cot of an Angle
Function
Angle (°)

What is sin 15°?

Answer

sin 15° =
(√6 − √2)/4 ≈ 0.2588

Angle in radians: 15° = π/12. The point of the angle is in quadrant I, where sine is positive.

≈ — rounded to 4 decimal places.

P(cos 15°, sin 15°) = ((√6 + √2)/4, (√6 − √2)/4)

sin 15° = sin(45° − 30°) = (√2/2)(√3/2) − (√2/2)(1/2) = (√6 − √2)/4

xyOP

P(cos 15°, sin 15°) ≈ (0.9659, 0.2588)

Highlighted: the projection on the y-axis — sine, y ≈ 0.2588.

All four functions of 15°
FunctionExact valueDecimal
sin 15°(√6 − √2)/4≈ 0.2588
cos 15°(√6 + √2)/4≈ 0.9659
tan 15°2 − √3≈ 0.2679
cot 15°2 + √3≈ 3.7321

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
12°≈ 0.2079
13°≈ 0.2250
14°≈ 0.2419
15°(√6 − √2)/4
16°≈ 0.2756
17°≈ 0.2924
18°(√5 − 1)/4

FAQ

What is sin 15°?

sin 15° = (√6 − √2)/4 ≈ 0.2588

How are sin 15° and cos 75° related?

They are equal: sin α = cos(90° − α), and 15° + 75° = 90°. So sin 15° = cos 75° = (√6 − √2)/4, cos 15° = sin 75° = (√6 + √2)/4, and tan 15° = cot 75° = 2 − √3.

Why does a calculator show 0.6503 for sin 15?

The calculator is in radian mode (RAD): it takes sin 15 as the sine of 15 radians, sin 15 rad ≈ 0.6503. Switch it to degrees (DEG): sin 15° = (√6 − √2)/4 ≈ 0.2588. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also