Answer
$\sin\theta=\frac{y}{r}=\frac{-6}{12}=-\frac{1}{2}$
$\cos\theta=\frac{x}{r}=\frac{6\sqrt 3}{12}=\frac{\sqrt 3}{2}$
$\csc\theta=\frac{r}{y}=\frac{12}{-6}=-2$
$\sec\theta=\frac{r}{x}=\frac{12}{6\sqrt 3}=\frac{2\sqrt 3}{3}$
$\tan\theta=\frac{y}{x}=\frac{-6}{6\sqrt 3}=-\frac{\sqrt 3}{3}$
$\cot\theta=\frac{x}{y}=\frac{6\sqrt 3}{-6}=-\sqrt 3$
Work Step by Step
$x=6\sqrt 3; y=-6$
$r=\sqrt {x^{2}+y^{2}}=\sqrt {(6\sqrt 3)^{2}+(-6)^{2}}=\sqrt {144}=12$
