Cos 15 Degrees

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

What is cos 15°?

Answer

cos 15° =
(√6 + √2)/4 ≈ 0.9659

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

≈ — rounded to 4 decimal places.

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

cos 15° = cos(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 x-axis — cosine, x ≈ 0.9659.

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 ↑

Cosine of nearby angles

Anglecos
12°≈ 0.9781
13°≈ 0.9744
14°≈ 0.9703
15°(√6 + √2)/4
16°≈ 0.9613
17°≈ 0.9563
18°√(10 + 2√5)/4

FAQ

What is cos 15°?

cos 15° = (√6 + √2)/4 ≈ 0.9659

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 −0.7597 for cos 15?

The calculator is in radian mode (RAD): it takes cos 15 as the cosine of 15 radians, cos 15 rad ≈ −0.7597. Switch it to degrees (DEG): cos 15° = (√6 + √2)/4 ≈ 0.9659. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also