Cot 120 Degrees

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

What is cot 120°?

Answer

cot 120° =
−√3/3 ≈ −0.5774

Angle in radians: 120° = 2π/3. The point of the angle is in quadrant II, where cotangent is negative.

≈ — rounded to 4 decimal places.

cot 120° = cot(180° − 60°) = −cot 60° = −√3/3

cot 120° = cos 120° / sin 120° = (−1/2) / (√3/2) = −√3/3

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

cot 60° = (1/2) / (√3/2) = 1/√3 = √3/3

xyOP

P(cos 120°, sin 120°) ≈ (−0.5, 0.8660)

C(cot 120°, 1) ≈ (−0.5774, 1) — where line OP meets the line y = 1.

All four functions of 120°
FunctionExact valueDecimal
sin 120°√3/2≈ 0.8660
cos 120°−1/2−0.5
tan 120°−√3≈ −1.7321
cot 120°−√3/3≈ −0.5774

Reference angle: cot 60° = √3/3

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
106°≈ −0.2867
108°−√(25 − 10√5)/5
110°≈ −0.3640
120°−√3/3
125°≈ −0.7002
126°−√(5 − 2√5)
127°≈ −0.7536

FAQ

What is cot 120°?

cot 120° = −√3/3 ≈ −0.5774

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 120° = −√3/3 ≈ −0.5774.

Why does a calculator show 1.4023 for cot 120?

The calculator is in radian mode (RAD): it takes cot 120 as the cotangent of 120 radians, cot 120 rad ≈ 1.4023. Switch it to degrees (DEG): cot 120° = −√3/3 ≈ −0.5774. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also