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Agata [3.3K]
2 years ago
15

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

Mathematics
1 answer:
IRINA_888 [86]2 years ago
7 0

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}.

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