Answer
$\tan{(-\frac{7\pi}{3})}= -\sqrt3$
Work Step by Step
The angle $-\dfrac{7\pi}{3}$ is in Quadrant IV.
Its reference angle is $\dfrac{\pi}{3}$.
Note that $\dfrac{\pi}{3}$ is a special angle and that $\tan{(\frac{\pi}{3})}=\sqrt3$.
The trigonometric function values of an angle and its reference angle are either the same or differ only in signs.
Since $-\dfrac{7\pi}{3}$ terminates in Quadrant IV, then its tangent is negative.
Therefore,
$\tan{(-\frac{7\pi}{3})}= -\sqrt3$.
