Cot 150 Degrees

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

What is cot 150°?

Answer

cot 150° =
−√3 ≈ −1.7321

Angle in radians: 150° = 5π/6. The point of the angle is in quadrant II, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 150° = cot(180° − 30°) = −cot 30° = −√3

cot 150° = cos 150° / sin 150° = (−√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 150°, sin 150°) ≈ (−0.8660, 0.5)

C(cot 150°, 1) ≈ (−1.7321, 1) — where line OP meets the line y = 1.

All four functions of 150°
FunctionExact valueDecimal
sin 150°1/20.5
cos 150°−√3/2≈ −0.8660
tan 150°−√3/3≈ −0.5774
cot 150°−√3≈ −1.7321

Reference angle: cot 30° = √3

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
142°≈ −1.2799
144°−√(25 + 10√5)/5
145°≈ −1.4281
150°−√3
159°≈ −2.6051
160°≈ −2.7475
162°−√(5 + 2√5)

FAQ

What is cot 150°?

cot 150° = −√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 150° = −√3 ≈ −1.7321.

Why does a calculator show −0.9781 for cot 150?

The calculator is in radian mode (RAD): it takes cot 150 as the cotangent of 150 radians, cot 150 rad ≈ −0.9781. Switch it to degrees (DEG): cot 150° = −√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