Answer
$-\sqrt3$
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 $\frac{5\pi}{6}$ 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,
$\cot{\frac{5\pi}{6}}
\\= \frac{x}{y}
\\=\dfrac{-\frac{\sqrt3}{2}}{\frac{1}{2}}
\\=-\frac{\sqrt3}{2} \cdot \frac{2}{1}
\\=-\sqrt3$
