Question

Find the exact value of cos 120° in simplest form with a rational
denominator.

Answer 1

Given:

cos 120°

To find:

The exact value of cos 120° in simplest form with a rational denominator.

Solution:

We have,

`\cos 120^\circ`

It can be written as

`\cos 120^\circ=\cos (90^\circ+30^\circ)`

`\cos 120^\circ=-\sin 30^\circ`
`[\because \cos (90^\circ-\theta)=-\sin \theta]`

`\cos 120^\circ=-\left((1)/(2)\right)`
`[\because \sin 30^\circ=(1)/(2)]`

`\cos 120^\circ=-(1)/(2)`

Therefore, the exact value of cos 120° is
`-(1)/(2)`.