What is the value of $\csc \left(\frac{11\pi }{6}\right)$?

We need to find the value of $\csc \left(\frac{11\pi }{6}\right)$.We can rewrite the angle $\frac{11\pi }{6}$ as:
$$\frac{11\pi }{6}=2\pi -\frac{\pi }{6}$$
Therefore:
$$\csc \left(\frac{11\pi }{6}\right)=\csc \left(2\pi -\frac{\pi }{6}\right)$$
Using the trigonometric identity $\csc (2\pi -\theta )=-\csc \theta$ (since the angle lies in the fourth quadrant where cosecant is negative):
$$\csc \left(2\pi -\frac{\pi }{6}\right)=-\csc \left(\frac{\pi }{6}\right)$$
We know that $\csc \left(\frac{\pi }{6}\right)=\frac{1}{\sin (\pi /6)}=\frac{1}{1/2}=2$.Hence:
$$\csc \left(\frac{11\pi }{6}\right)=-2$$