Answer
- $\frac{\sqrt 3}{2}$
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 III,
The reference angle = $ 180^{\circ} - 150^{\circ} $ = $30^{\circ}$
As $ (-150)^{\circ}$ terminates in quadrant III, its $\cos$ will be negative. Therefore by reference angle theorem-
$\cos (-150)^{\circ}$ = - $\cos 30^{\circ}$
= - $\frac{\sqrt 3}{2}$
