Answer
$sin\theta= -\frac{2\sqrt {2}}{3}$,
$cos\theta= \frac{1}{3}$,
$tan\theta= -2\sqrt {2}$,
$cot\theta= -\frac{\sqrt {2}}{4}$,
$csc\theta= -\frac{3\sqrt {2}}{4}$.
Work Step by Step
Given $sec\theta=3$ and $\theta$ is in quadrant IV, let $r=3, x=1$, we have $y=-\sqrt {(3)^2-(1)^2}=-2\sqrt {2}$, thus:
$sin\theta=\frac{y}{r}=-\frac{2\sqrt {2}}{3}$,
$cos\theta=\frac{x}{r}=\frac{1}{3}$,
$tan\theta=\frac{y}{x}=-2\sqrt {2}$,
$cot\theta=\frac{1}{tan\theta}=-\frac{\sqrt {2}}{4}$,
$csc\theta=\frac{1}{sin\theta}=-\frac{3\sqrt {2}}{4}$.
