Cot 210 Degrees

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

What is cot 210°?

Answer

cot 210° =
√3 ≈ 1.7321

Angle in radians: 210° = 7π/6. The point of the angle is in quadrant III, where cotangent is positive.

≈ — rounded to 4 decimal places.

cot 210° = cot(180° + 30°) = cot 30° = √3

cot 210° = cos 210° / sin 210° = (−√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 210°, sin 210°) ≈ (−0.8660, −0.5)

C(cot 210°, 1) ≈ (1.7321, 1) — where line OP meets the line y = 1, on the extension of the ray beyond O (dashed).

All four functions of 210°
FunctionExact valueDecimal
sin 210°−1/2−0.5
cos 210°−√3/2≈ −0.8660
tan 210°√3/3≈ 0.5774
cot 210°√3≈ 1.7321

Reference angle: cot 30° = √3

See Also

Recalculate with different values ↑

Cotangent of nearby angles

Anglecot
195°2 + √3
198°√(5 + 2√5)
200°≈ 2.7475
210°√3
211°≈ 1.6643
215°≈ 1.4281
216°√(25 + 10√5)/5

FAQ

What is cot 210°?

cot 210° = √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 210° = √3 ≈ 1.7321.

Why does a calculator show −1.8898 for cot 210?

The calculator is in radian mode (RAD): it takes cot 210 as the cotangent of 210 radians, cot 210 rad ≈ −1.8898. Switch it to degrees (DEG): cot 210° = √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