Sin 120 Degrees

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

What is sin 120°?

Answer

sin 120° =
√3/2 ≈ 0.8660

Angle in radians: 120° = 2π/3. The point of the angle is in quadrant II, where sine is positive.

≈ — rounded to 4 decimal places.

sin 120° = sin(180° − 60°) = sin 60° = √3/2

P(cos 120°, sin 120°) = (−1/2, √3/2)

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

sin 60° = √(1 − 1/4) = √3/2

xyOP

P(cos 120°, sin 120°) ≈ (−0.5, 0.8660)

Highlighted: the projection on the y-axis — sine, y ≈ 0.8660.

All four functions of 120°
FunctionExact valueDecimal
sin 120°√3/2≈ 0.8660
cos 120°−1/2−0.5
tan 120°−√3≈ −1.7321
cot 120°−√3/3≈ −0.5774

Reference angle: sin 60° = √3/2

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
106°≈ 0.9613
108°√(10 + 2√5)/4
110°≈ 0.9397
120°√3/2
125°≈ 0.8192
126°(√5 + 1)/4
127°≈ 0.7986

FAQ

What is sin 120°?

sin 120° = √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: sin 120° = √3/2 ≈ 0.8660.

Why does a calculator show 0.5806 for sin 120?

The calculator is in radian mode (RAD): it takes sin 120 as the sine of 120 radians, sin 120 rad ≈ 0.5806. Switch it to degrees (DEG): sin 120° = √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