Answer
$-2$
Work Step by Step
RECALL:
$\sin{s} = y
\\\cos{s} = x
\\\tan{s} = \frac{y}{x}
\\\cot{s} = \frac{x}{y}
\\\sec{s} = \frac{1}{x}
\\\csc{s}=\frac{1}{y}$
(refer to Figure 11 on page 111 of the textbook)
The angle $\frac{11\pi}{6}$ intersects the unit circle at the point $(\frac{\sqrt3}{2}, -\frac{1}{2})$.
This point has:
$x= \frac{\sqrt3}{2}$
$y=-\frac{1}{2}$
Thus,
$\csc{\frac{11\pi}{6}} = \frac{1}{y}=\dfrac{1}{-\frac{1}{2}}=-2$
