Cos 210 Degrees

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

What is cos 210°?

Answer

cos 210° =
−√3/2 ≈ −0.8660

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

≈ — rounded to 4 decimal places.

cos 210° = cos(180° + 30°) = −cos 30° = −√3/2

P(cos 210°, sin 210°) = (−√3/2, −1/2)

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

cos 30° = √(1 − 1/4) = √3/2

xyOP

P(cos 210°, sin 210°) ≈ (−0.8660, −0.5)

Highlighted: the projection on the x-axis — cosine, x ≈ −0.8660.

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: cos 30° = √3/2

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
195°−(√6 + √2)/4
198°−√(10 + 2√5)/4
200°≈ −0.9397
210°−√3/2
211°≈ −0.8572
215°≈ −0.8192
216°−(√5 + 1)/4

FAQ

What is cos 210°?

cos 210° = −√3/2 ≈ −0.8660

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: cos 210° = −√3/2 ≈ −0.8660.

Why does a calculator show −0.8839 for cos 210?

The calculator is in radian mode (RAD): it takes cos 210 as the cosine of 210 radians, cos 210 rad ≈ −0.8839. Switch it to degrees (DEG): cos 210° = −√3/2 ≈ −0.8660. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also