# What is the value of cos 120°?

In any right-angled triangle, the cosine of an angle is the length of the adjacent side divided by the length of the hypotenuse.

## Answer: The value of cos 120° degree is -1/2.

Let us proceed step by step.

**Explanation:**

cos 120° can also be written as sum of 90° and 30°.

After writing cos120° as the sum of two angles, we can use trigonometric identity ;

cos (α + b) = cos α cos b - sin α sin b

Substituting the value of a as 90° and b as 30°,

cos (90° + 30°) = cos 90° cos 30° - sin 90° sin 30°

cos (90° + 30°) = (0 - 1/2)

cos (90° + 30°) = -1/2

cos 120° = -1/2