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