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

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

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

$\cos 120^\circ=-\left(\dfrac{1}{2}\right)$             $[\because \sin 30^\circ=\dfrac{1}{2}]$

$\cos 120^\circ=-\dfrac{1}{2}$

Therefore, the exact value of cos 120° is $-\dfrac{1}{2}$.