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