Answer
$\sin\theta=\frac{y}{r}=\frac{\sqrt {3}}{5}$
$\cos\theta=\frac{x}{r}=\frac{-\sqrt {22}}{5}=-\frac{\sqrt {22}}{5}$
$\csc\theta=\frac{r}{y}=\frac{5}{\sqrt {3}}=\frac{5\sqrt 3}{3}$
$\sec\theta=\frac{r}{x}=\frac{5}{-\sqrt {22}}=-\frac{5\sqrt {22}}{22}$
$\tan\theta=\frac{y}{x}=\frac{\sqrt {3}}{-\sqrt {22}}=-\frac{\sqrt {66}}{22}$
$\cot\theta=\frac{x}{y}=\frac{-\sqrt {22}}{\sqrt {3}}=-\frac{\sqrt {66}}{3}$
Work Step by Step
From sine we know that $y=\sqrt 3; r=5$, so lets find x:
$x^{2}+y^{2}=r^{2}$
$x^{2}+(\sqrt 3)^{2}=5^{2}$
$x^{2}+3=25$
$x^{2}=22$ (since $\cos\theta\lt0$)
$x=\sqrt {22}$
