## Trigonometry (11th Edition) Clone

$-2$
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, $\sec{(\frac{8\pi}{3})} = \dfrac{1}{-\frac{1}{2}}=-2$