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