Given:
cos 120°
To find:
The exact value of cos 120° in simplest form with a rational denominator.
Solution:
We have,
[tex]\cos 120^\circ[/tex]
It can be written as
[tex]\cos 120^\circ=\cos (90^\circ+30^\circ)[/tex]
[tex]\cos 120^\circ=-\sin 30^\circ[/tex] [tex][\because \cos (90^\circ-\theta)=-\sin \theta][/tex]
[tex]\cos 120^\circ=-\left(\dfrac{1}{2}\right)[/tex] [tex][\because \sin 30^\circ=\dfrac{1}{2}][/tex]
[tex]\cos 120^\circ=-\dfrac{1}{2}[/tex]
Therefore, the exact value of cos 120° is [tex]-\dfrac{1}{2}[/tex].
