Answer
$\sin\theta=\frac{y}{r}=\frac{-2}{4}=-\frac{1}{2}$
$\cos\theta=\frac{x}{r}=\frac{-2\sqrt 3}{4}=-\frac{\sqrt 3}{2}$
$\tan\theta=\frac{y}{x}=\frac{-2}{-2\sqrt3}=\frac{\sqrt 3}{3}$
$\csc\theta=\frac{r}{y}=\frac{4}{-2}=-2$
$\sec\theta=\frac{r}{x}=\frac{4}{-2\sqrt 3}=-\frac{2\sqrt 3}{3}$
$\cot\theta=\frac{x}{y}=\frac{-2\sqrt 3}{-2}=\sqrt 3$
Work Step by Step
$x=-2\sqrt 3$
$y=-2$
$r=\sqrt{(-2)^{2}+(-2\sqrt 3)^{2}}=\sqrt {4+12}= 4$
