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

User Tarlen
by
7.7k points

1 Answer

13 votes

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).

User Jeff Marino
by
8.9k points

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