Sin 210 Degrees

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

What is sin 210°?

Answer

sin 210° =
−1/2 = −0.5

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

sin 210° = sin(180° + 30°) = −sin 30° = −1/2

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.

sin 30° = 1/2

xyOP

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

Highlighted: the projection on the y-axis — sine, y = −0.5.

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: sin 30° = 1/2

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
195°−(√6 − √2)/4
198°−(√5 − 1)/4
200°≈ −0.3420
210°−1/2
211°≈ −0.5150
215°≈ −0.5736
216°−√(10 − 2√5)/4

FAQ

What is sin 210°?

sin 210° = −1/2 = −0.5

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: sin 210° = −1/2 = −0.5.

Why does a calculator show 0.4677 for sin 210?

The calculator is in radian mode (RAD): it takes sin 210 as the sine of 210 radians, sin 210 rad ≈ 0.4677. Switch it to degrees (DEG): sin 210° = −1/2 = −0.5. In radians the value is never undefined: π is irrational, so a whole number of radians never lands exactly on an axis.

See Also