Cot 30 Degrees

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

What is cot 30°?

Answer

cot 30° =
√3 ≈ 1.7321

Angle in radians: 30° = π/6. The point of the angle is in quadrant I, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 30° = cos 30° / sin 30° = (√3/2) / (1/2) = √3

Half of an equilateral triangle with side 1: the hypotenuse is 1 and the leg opposite 30° is 1/2.

cot 30° = (√3/2) / (1/2) = √3

xyOP

P(cos 30°, sin 30°) ≈ (0.8660, 0.5)

C(cot 30°, 1) ≈ (1.7321, 1) — where line OP meets the line y = 1.

All four functions of 30°
FunctionExact valueDecimal
sin 30°1/20.5
cos 30°√3/2≈ 0.8660
tan 30°√3/3≈ 0.5774
cot 30°√3≈ 1.7321

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
27°≈ 1.9626
28°≈ 1.8807
29°≈ 1.8040
30°√3
31°≈ 1.6643
32°≈ 1.6003
33°≈ 1.5399

FAQ

What is cot 30°?

cot 30° = √3 ≈ 1.7321

How to remember sin 30°, sin 45° and sin 60°?

Write them as √1/2, √2/2, √3/2: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2. Cosines are the same numbers in reverse order: cos 30° = √3/2, cos 45° = √2/2, cos 60° = 1/2; tan = sin / cos and cot = cos / sin. Here: cot 30° = √3 ≈ 1.7321.

Why does a calculator show −0.1561 for cot 30?

The calculator is in radian mode (RAD): it takes cot 30 as the cotangent of 30 radians, cot 30 rad ≈ −0.1561. Switch it to degrees (DEG): cot 30° = √3 ≈ 1.7321. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also