Answer
$sin\theta= \frac{\sqrt {5}}{5}$,
$cos\theta= -\frac{2\sqrt {5}}{5}$,
$tan\theta= -\frac{1}{2}$,
$sec\theta= -\frac{\sqrt {5}}{2}$,
$csc\theta= \sqrt 5$.
Work Step by Step
Given $cot\theta=-2$ and $\theta$ is in quadrant II, let $x=-2, y=1$, we have $r=\sqrt {(-2)^2+(1)^2}=\sqrt {5}$, thus:
$sin\theta=\frac{y}{r}=\frac{\sqrt {5}}{5}$,
$cos\theta=\frac{x}{r}=-\frac{2\sqrt {5}}{5}$,
$tan\theta=\frac{y}{x}=-\frac{1}{2}$,
$sec\theta=\frac{1}{cos\theta}=-\frac{\sqrt {5}}{2}$,
$csc\theta=\frac{1}{sin\theta}=\sqrt 5$.
