Answer
$sin(\theta) =-\frac{12}{13}$,
$cos(\theta) =\frac{5}{13}$,
$tan(\theta) =-\frac{12}{5}$,
$cot(\theta) =-\frac{5}{12}$,
$sec(\theta) =\frac{13}{5}$,
$csc(\theta) =-\frac{13}{12}$.
Work Step by Step
Given $x=5,y=-12$, the terminal side is in quadrant IV with $r=\sqrt {x^2+y^2}=13$, we have:
$sin(\theta)=\frac{y}{r}=-\frac{12}{13}$,
$cos(\theta)=\frac{x}{r}=\frac{5}{13}$,
$tan(\theta)=\frac{y}{x}=-\frac{12}{5}$,
$cot(\theta)=\frac{x}{y}=-\frac{5}{12}$,
$sec(\theta)=\frac{r}{x}=\frac{13}{5}$,
$csc(\theta)=\frac{r}{y}=-\frac{13}{12}$.
