Answer
Exact value of $\cos 150^{\circ}$ = - $\frac{\sqrt 3}{2}$
Work Step by Step
To find exact value of $\cos 150^{\circ}$, let's find its reference angle first. As $ 150^{\circ}$ terminates in quadrant II,
The reference angle = $ 180^{\circ} - 150^{\circ}$ = $30^{\circ}$
As $ 150^{\circ}$ terminates in quadrant II, its cos will be negative. Therefore by reference angle theorem-
$\cos 150^{\circ}$ = - $\cos30^{\circ}$
= - $\frac{\sqrt 3}{2}$