Answer
$sin\theta= -\frac{3}{5}$,
$cos\theta= -\frac{4}{5}$,
$tan\theta= \frac{3}{4}$,
$sec\theta= -\frac{5}{4}$,
$csc\theta= -\frac{5}{3}$.
Work Step by Step
Given $cot\theta=\frac{4}{3}$, let $x=4,y=3$, we can get $r=\sqrt {x^2+y^2}=5$. Use the fact that $cos\theta\lt0,cot\theta\gt0\longrightarrow \theta$ is in quadrant III to determine the sign of each function:
$sin\theta=-\frac{y}{r}=-\frac{3}{5}$,
$cos\theta=-\frac{x}{r}=-\frac{4}{5}$,
$tan\theta=\frac{y}{x}=\frac{3}{4}$,
$sec\theta=-\frac{r}{x}=-\frac{5}{4}$,
$csc\theta=-\frac{r}{y}=-\frac{5}{3}$.
