#### Answer

$\cos{(-\frac{7\pi}{6})} = -\frac{\sqrt3}{2}$

#### Work Step by Step

Recall:
(1) An angle and its reference angle either have the same trigonometric function values or differ only in signs.
(2) $\frac{\pi}{6}$ is a special angle whose cosine value is known to be $\frac{\sqrt3}{2}$.
Note that the reference angle of $-\frac{7\pi}{6}$ is $\frac{\pi}{6}$.
However, since $-\frac{7\pi}{6}$ is in Quadrant II, then its cosine value is negative.
Therefore,
$\cos{(-\frac{7\pi}{6})} = -\frac{\sqrt3}{2}$