Answer
$\sin\theta=\frac{y}{r}=\frac{2}{4}=\frac{1}{2}$
$\cos\theta=\frac{x}{r}=\frac{-2\sqrt 3}{4}=-\frac{\sqrt 3}{2}$
$\tan\theta=\frac{y}{x}=\frac{2}{-2\sqrt 3}=-\frac{\sqrt 3}{3}$
$\csc\theta=\frac{r}{y}=\frac{4}{2}=2$
$\sec\theta=\frac{r}{x}=\frac{4}{-2 \sqrt 3}=-\frac{2\sqrt 3}{3}$
$\cot\theta=\frac{x}{y}=\frac{-2\sqrt 3}{2}=-\sqrt 3$
Work Step by Step
$x=-2\sqrt 3$
$y=2$
$r=\sqrt{(-2\sqrt 3)^{2}+(2)^{2}}=\sqrt {12+4}= 4$
