Answer
See below
Work Step by Step
Substitute $(5,-\sqrt 11)$ into $x^2+y^2=r^2$ to find $r$:
$$x^2+y^2=r^2\\5^2+(-\sqrt 11)^2=r^2\\r^2=\sqrt 36\\r=\pm \sqrt 6\\r=\sqrt 6$$
$\sin \theta=\frac{y}{r}=\frac{-\sqrt 11}{6}$
$\cos \theta=\frac{x}{r}=\frac{5}{6}$
$\csc \theta=\frac{r}{y}=\frac{-6\sqrt 11}{11}$
$\sec \theta=\frac{r}{x}=\frac{6}{5}$
$\tan \theta=\frac{y}{x}=\frac{-\sqrt 11}{5}$
$\cot \theta=\frac{x}{y}=\frac{-5\sqrt 11}{11}$
