Answer
$cos\theta= -\frac{12}{13}$,
$tan\theta= \frac{5}{12}$,
$cot\theta= \frac{12}{5}$,
$sec\theta= -\frac{13}{12}$,
$csc\theta= -\frac{13}{5}$.
Work Step by Step
Given $sin\theta=-\frac{5}{13}$, let $y=5, r=13$, we can get $x=\sqrt {r^2-y^2}=12$. Use the fact that $\theta$ is in quadrant III to determine the sign of each function, we have:
$cos\theta=-\frac{x}{r}=-\frac{12}{13}$,
$tan\theta=\frac{y}{x}=\frac{5}{12}$,
$cot\theta=\frac{x}{y}=\frac{12}{5}$,
$sec\theta=-\frac{r}{x}=-\frac{13}{12}$,
$csc\theta=-\frac{r}{y}=-\frac{13}{5}$.
