Sin 150 Degrees

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

What is sin 150°?

Answer

sin 150° =
1/2 = 0.5

Angle in radians: 150° = 5π/6. The point of the angle is in quadrant II, where sine is positive.

sin 150° = sin(180° − 30°) = sin 30° = 1/2

P(cos 150°, sin 150°) = (−√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 150°, sin 150°) ≈ (−0.8660, 0.5)

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

All four functions of 150°
FunctionExact valueDecimal
sin 150°1/20.5
cos 150°−√3/2≈ −0.8660
tan 150°−√3/3≈ −0.5774
cot 150°−√3≈ −1.7321

Reference angle: sin 30° = 1/2

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
142°≈ 0.6157
144°√(10 − 2√5)/4
145°≈ 0.5736
150°1/2
159°≈ 0.3584
160°≈ 0.3420
162°(√5 − 1)/4

FAQ

What is sin 150°?

sin 150° = 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 150° = 1/2 = 0.5.

Why does a calculator show −0.7149 for sin 150?

The calculator is in radian mode (RAD): it takes sin 150 as the sine of 150 radians, sin 150 rad ≈ −0.7149. Switch it to degrees (DEG): sin 150° = 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