Answer
$sin\theta =\frac{5}{13}$
$cos\theta =-\frac{12}{13}$
$tan\theta =-\frac{5}{12}$
$cot\theta =-\frac{12}{5}$
$sec\theta =-\frac{13}{12}$
$csc\theta =\frac{13}{5}$
Work Step by Step
Given $x=-12,y=5$, we have $r=\sqrt {x^2+y^2}=13$:
$sin\theta=\frac{y}{r}=\frac{5}{13}$
$cos\theta=\frac{x}{r}=-\frac{12}{13}$
$tan\theta=\frac{y}{x}=-\frac{5}{12}$
$cot\theta=\frac{x}{y}=-\frac{12}{5}$
$sec\theta=\frac{r}{x}=-\frac{13}{12}$
$csc\theta=\frac{r}{y}=\frac{13}{5}$
