Answer
$\sin\theta=\frac{y}{r}=\frac{-2}{5}$
$\cos\theta=\frac{x}{r}=\frac{-\sqrt {21}}{5}$
$\csc\theta=\frac{r}{y}=\frac{5}{-2}$
$\sec\theta=\frac{r}{x}=\frac{5}{-\sqrt {21}}=-\frac{5\sqrt {21}}{21}$
$\tan\theta=\frac{y}{x}=\frac{-2}{-\sqrt {21}}=\frac{2\sqrt {21}}{21}$
$\cot\theta=\frac{x}{y}=\frac{-\sqrt {21}}{-2}=\frac{\sqrt {21}}{2}$
Work Step by Step
From sine we know quadrant that $y=-2; r=5$, so lets find x:
$x^{2}+y^{2}=r^{2}$
$x^{2}+(-2)^{2}=5^{2}$
$x^{2}+4=25$
$x^{2}=21$ (since $x\lt0$ in second quadrant)
$x=-\sqrt {21}$
