Cot 240 Degrees

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

What is cot 240°?

Answer

cot 240° =
√3/3 ≈ 0.5774

Angle in radians: 240° = 4π/3. The point of the angle is in quadrant III, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 240° = cot(180° + 60°) = cot 60° = √3/3

cot 240° = cos 240° / sin 240° = (−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 240°, sin 240°) ≈ (−0.5, −0.8660)

C(cot 240°, 1) ≈ (0.5774, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

All four functions of 240°
FunctionExact valueDecimal
sin 240°−√3/2≈ −0.8660
cos 240°−1/2−0.5
tan 240°√3≈ 1.7321
cot 240°√3/3≈ 0.5774

Reference angle: cot 60° = √3/3

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
225°1
227°≈ 0.9325
234°√(5 − 2√5)
240°√3/3
252°√(25 − 10√5)/5
255°2 − √3
270°0

FAQ

What is cot 240°?

cot 240° = √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 240° = √3/3 ≈ 0.5774.

Why does a calculator show 0.3446 for cot 240?

The calculator is in radian mode (RAD): it takes cot 240 as the cotangent of 240 radians, cot 240 rad ≈ 0.3446. Switch it to degrees (DEG): cot 240° = √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