Answer
$csc\theta = \sqrt 10$
Work Step by Step
Note:
$sin\theta = \frac{opp}{hyp}$
$cos\theta = \frac{adj}{hyp}$
$tan\theta = \frac{opp}{adj}$
$cot\theta = -3$
The equivalent is:
$tan\theta = \frac{-1}{3}$
We must find the Hypotenuse:
$\sqrt {1^{2}+3^{2}} = \sqrt 10$
We can then solve for $csc\theta$:
$sin\theta = \frac{1}{\sqrt 10}$
Therefore,
$csc\theta = \sqrt 10$
