Cos 120 Degrees

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

What is cos 120°?

Answer

cos 120° =
−1/2 = −0.5

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

cos 120° = cos(180° − 60°) = −cos 60° = −1/2

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.

cos 60° = 1/2

xyOP

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

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

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: cos 60° = 1/2

See Also

Recalculate with different values ↑

Cosine of nearby angles

Anglecos
106°≈ −0.2756
108°−(√5 − 1)/4
110°≈ −0.3420
120°−1/2
125°≈ −0.5736
126°−√(10 − 2√5)/4
127°≈ −0.6018

FAQ

What is cos 120°?

cos 120° = −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 120° = −1/2 = −0.5.

Why does a calculator show 0.8142 for cos 120?

The calculator is in radian mode (RAD): it takes cos 120 as the cosine of 120 radians, cos 120 rad ≈ 0.8142. Switch it to degrees (DEG): cos 120° = −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