find the exact values below. if applicable, click on \undefined\.\n \tan\frac{11pi}{6}=\n csc\frac{11pi}{6}=

Explanation:

Step1: Rewrite the angle

We know that $\frac{11\pi}{6}=2\pi - \frac{\pi}{6}$.

Step2: Find the value of $\tan\frac{11\pi}{6}$

Since $\tan(2\pi - \alpha)=-\tan\alpha$, then $\tan\frac{11\pi}{6}=\tan(2\pi - \frac{\pi}{6})=-\tan\frac{\pi}{6}=-\frac{\sqrt{3}}{3}$.

Step3: Find the value of $\csc\frac{11\pi}{6}$

First, $\sin\frac{11\pi}{6}=\sin(2\pi - \frac{\pi}{6})=-\sin\frac{\pi}{6}=-\frac{1}{2}$. And $\csc\theta=\frac{1}{\sin\theta}$, so $\csc\frac{11\pi}{6}=\frac{1}{\sin\frac{11\pi}{6}}=- 2$.

Answer:

$\tan\frac{11\pi}{6}=-\frac{\sqrt{3}}{3}$, $\csc\frac{11\pi}{6}=-2$