Answer
$cot~\theta=-\frac{\sqrt {5}}{2}$
$tan~\theta=-\frac{2\sqrt {5}}{5}$
$sec^2\theta=-\frac{3\sqrt {5}}{5}$
$cos~\theta=-\frac{\sqrt 5}{3}$
$sin~\theta=\frac{2}{3}$
Work Step by Step
$csc^2\theta=1+cot^2\theta$
$cot^2\theta=(\frac{3}{2})^2-1=\frac{5}{4}$
$cot~\theta=-\frac{\sqrt {5}}{2}~~~~$ $(sin~\theta\gt0$ and $cos~\theta\lt0)$
$tan~\theta=\frac{1}{cot~\theta}=-\frac{2}{\sqrt {5}}=-\frac{2\sqrt {5}}{5}$
$sec^2\theta=tan^2\theta+1=\frac{4}{5}+1=\frac{9}{5}$
$sec~\theta=-\frac{3}{\sqrt {5}}=-\frac{3\sqrt {5}}{5}$
$cos~\theta=\frac{1}{sec~\theta}=-\frac{\sqrt 5}{3}$
$sin~\theta=\frac{1}{csc~\theta}=\frac{2}{3}$
