Sin 240 Degrees

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

What is sin 240°?

Answer

sin 240° =
−√3/2 ≈ −0.8660

Angle in radians: 240° = 4π/3. The point of the angle is in quadrant III, where sine is negative.

≈ — rounded to 4 decimal places.

sin 240° = sin(180° + 60°) = −sin 60° = −√3/2

P(cos 240°, sin 240°) = (−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 240°, sin 240°) ≈ (−0.5, −0.8660)

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

All four functions of 240°
FunctionExact valueDecimal
sin 240°−√3/2≈ −0.8660
cos 240°−1/2−0.5
tan 240°√3≈ 1.7321
cot 240°√3/3≈ 0.5774

Reference angle: sin 60° = √3/2

See Also

Recalculate with different values ↑

Sine of nearby angles

Anglesin
225°−√2/2
227°≈ −0.7314
234°−(√5 + 1)/4
240°−√3/2
252°−√(10 + 2√5)/4
255°−(√6 + √2)/4
270°−1

FAQ

What is sin 240°?

sin 240° = −√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 240° = −√3/2 ≈ −0.8660.

Why does a calculator show 0.9454 for sin 240?

The calculator is in radian mode (RAD): it takes sin 240 as the sine of 240 radians, sin 240 rad ≈ 0.9454. Switch it to degrees (DEG): sin 240° = −√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