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 $r=\sqrt {(-12)^2+5^2}=13$. Thus
$sin\theta=\frac{y}{r}=\frac{5}{13}$,
$cos\theta=\frac{x}{r}=-\frac{12}{13}$,
$tan\theta=\frac{y}{x}=-\frac{5}{12}$,
$cot\theta=\frac{x}{y}=-\frac{12}{5}$,
$sec\theta=\frac{r}{x}=\frac{13}{12}$,
$csc\theta=\frac{r}{y}=-\frac{13}{5}$.
