Answer
$\cos$ -510$^{\circ}$ = $\frac{-\sqrt3}{2}$
Work Step by Step
$\cos$ -510$^{\circ}$
First, lets find the coterminal angle.
-510$^{\circ}$ - 360$^{\circ}$ = -150$^{\circ}$
Next, we find the reference angle.
$\theta$$^{1}$ = 180$^{\circ}$ - 150$^{\circ}$ = 30$^{\circ}$
Since the coterminal angle is in Quadrant III, $\cos$ is negative.
Therefore:
$\cos$ 30$^{\circ}$ = $\frac{-\sqrt3}{2}$
