Cot 15 Degrees

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

What is cot 15°?

Answer

cot 15° =
2 + √3 ≈ 3.7321

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

≈ — rounded to 4 decimal places.

cot 15° = cos 15° / sin 15° = ((√6 + √2)/4) / ((√6 − √2)/4) = 2 + √3

cot 15° = 1 / tan 15° = 1 / (2 − √3) = 2 + √3

xyOP

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

C(cot 15°, 1) ≈ (3.7321, 1) — where line OP meets the line y = 1; C is beyond the drawing, the arrow points to it.

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 ↑

Cotangent of nearby angles

Anglecot
12°≈ 4.7046
13°≈ 4.3315
14°≈ 4.0108
15°2 + √3
16°≈ 3.4874
17°≈ 3.2709
18°√(5 + 2√5)

FAQ

What is cot 15°?

cot 15° = 2 + √3 ≈ 3.7321

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 −1.1682 for cot 15?

The calculator is in radian mode (RAD): it takes cot 15 as the cotangent of 15 radians, cot 15 rad ≈ −1.1682. Switch it to degrees (DEG): cot 15° = 2 + √3 ≈ 3.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also