Answer
See below
Work Step by Step
Substitute $(2,-2)$ into $x^2+y^2=r^2$ to find $r$:
$$x^2+y^2=r^2\\2^2+(-2)^2=r^2\\r^2=8\\r=\pm 2\sqrt 2\\r=2\sqrt 2$$
$\sin \theta=\frac{y}{r}=-\frac{2}{\sqrt 2}=-\frac{2\sqrt 2}{2}$
$\cos \theta=\frac{x}{r}=\frac{\sqrt 2}{2}$
$\csc \theta=\frac{r}{y}=\frac{-2\sqrt 2}{2}=-\sqrt 2$
$\sec \theta=\frac{r}{x}=\sqrt 2$
$\tan \theta=\frac{y}{x}=-1$
$\cot \theta=\frac{x}{y}=-1$
