Answer
$\cot\theta=\sqrt 3$
Work Step by Step
1.We get this information from the given cosecant value
$y=-1$
$r=2$
2. We can use y and r to find x (we need to remember that sign of x depends on quadrant, since it ends in quadrant III, x must be negative)
$r=\sqrt {y^{2}+x^{2}}$
$x=-\sqrt {r^{2}-y^{2}}=-\sqrt {(2)^{2}-(-1)^{2}}=-\sqrt {3}$
4. Then insert values,
$\cot\theta=\sqrt 3$
