Answer
Exact value of $\cos 660^{\circ} = \frac{1}{2} $
Work Step by Step
To find exact value of $\cos 660^{\circ}$, let's find its reference angle first.
$ 660^{\circ} = 360^{\circ} + 300^{\circ}$
As $ 300^{\circ}$ terminates in quadrant IV, $ 660^{\circ}$ will also terminate in quadrant IV with the same reference angle.
The reference angle of $ 300^{\circ}$ and hence $ 660^{\circ}$= $ 360^{\circ} - 300^{\circ}$ = $60^{\circ}$
As $ 660^{\circ}$ terminates in quadrant IV, its cos will be positive. Therefore by reference angle theorem-
$\cos 660^{\circ}$ = $\cos 60^{\circ}$
= $\frac{1}{2}$
