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