which of the following best explains why $\tan\frac{5pi}{6}\neq\tan\frac{5pi}{3}$?\nthe angles do not have…

Brief Explanations:

First, find the reference - angles and signs of $\tan\frac{5\pi}{6}$ and $\tan\frac{5\pi}{3}$. The angle $\frac{5\pi}{6}$ is in the second quadrant where tangent is negative, and its reference angle is $\pi-\frac{5\pi}{6}=\frac{\pi}{6}$. The angle $\frac{5\pi}{3}$ is in the fourth quadrant where tangent is negative, and its reference angle is $2\pi - \frac{5\pi}{3}=\frac{\pi}{3}$. Since the reference - angles are different ($\frac{\pi}{6}\neq\frac{\pi}{3}$) and the signs are the same (both negative), the main reason $\tan\frac{5\pi}{6}\neq\tan\frac{5\pi}{3}$ is that they do not have the same reference angle.

Answer:

The angles do not have the same reference angle.