Answer
$tan\theta =-\frac{1}{3}$,
$cot\theta =-3$,
$sec\theta =\frac{\sqrt {10}}{3}$,
$csc\theta =-\sqrt {10}$.
Work Step by Step
1. As $sin\theta\lt0, cos\theta\gt0$, we can identify $\theta$ is in quadrant IV.
2. Let $x=3, y=-1, r=\sqrt {10}$, we have:
$tan\theta=\frac{y}{x}=-\frac{1}{3}$,
$cot\theta=\frac{x}{y}=-3$,
$sec\theta=\frac{r}{x}=\frac{\sqrt {10}}{3}$,
$csc\theta=\frac{r}{y}=-\sqrt {10}$.
