Answer
Exact value of $\cos 570^{\circ}$= $\frac{\sqrt 3}{2}$
Work Step by Step
To find exact value of $\cos 570^{\circ}$, let's find its reference angle first.
$ 570^{\circ} = 360^{\circ} + 210^{\circ}$
As $ 210^{\circ}$ terminates in quadrant III, $ 570^{\circ}$ will also terminate in quadrant III with the same reference angle.
The reference angle = $ 210^{\circ} - 180^{\circ}$ = $30^{\circ}$
As $ 570^{\circ}$ terminates in quadrant III, its cos will be positive. Therefore by reference angle theorem-
$\cos 570^{\circ}$ = $\cos30^{\circ}$
= $\frac{\sqrt 3}{2}$
