Cos 240 Degrees

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

What is cos 240°?

Answer

cos 240° =
−1/2 = −0.5

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

cos 240° = cos(180° + 60°) = −cos 60° = −1/2

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.

cos 60° = 1/2

xyOP

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

Highlighted: the projection on the x-axis — cosine, x = −0.5.

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: cos 60° = 1/2

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
225°−√2/2
227°≈ −0.6820
234°−√(10 − 2√5)/4
240°−1/2
252°−(√5 − 1)/4
255°−(√6 − √2)/4
270°0

FAQ

What is cos 240°?

cos 240° = −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: cos 240° = −1/2 = −0.5.

Why does a calculator show 0.3258 for cos 240?

The calculator is in radian mode (RAD): it takes cos 240 as the cosine of 240 radians, cos 240 rad ≈ 0.3258. Switch it to degrees (DEG): cos 240° = −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