Answer
$-2$
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) $\sec{\theta} = \dfrac{1}{\cos{\theta}}$
$\frac{\pi}{3}$ is a special angle whose cosine value is known to be $\frac{1}{2}$.
Note that the reference angle of $\frac{8\pi}{3}$ is $\frac{\pi}{3}$.
However, since $\frac{8\pi}{3}$ is in Quadrant II, then its cosine value is negative.
Therefore,
$\sec{(\frac{8\pi}{3})} = \dfrac{1}{-\frac{1}{2}}=-2$
