Answer
$sin\theta =-\frac{2\sqrt 5}{5}$,
$cos\theta= \frac{\sqrt 5}{5}$,
$cot\theta= -\frac{1}{2}$,
$sec\theta= \sqrt 5$,
$csc\theta= -\frac{\sqrt 5}{2}$.
Work Step by Step
Given $tan\theta=-2$ and $\theta$ in quadrant IV, we have $x=1,y=-2, r=\sqrt 5$.
$sin\theta=\frac{y}{r}=-\frac{2\sqrt 5}{5}$,
$cos\theta=\frac{x}{r}=\frac{\sqrt 5}{5}$,
$cot\theta=\frac{x}{y}=-\frac{1}{2}$,
$sec\theta=\frac{r}{x}=\sqrt 5$,
$csc\theta=\frac{r}{y}=-\frac{\sqrt 5}{2}$.
