Answer
$sin\theta= \frac{2\sqrt 2}{3}$,
$tan\theta= =-2\sqrt 2$,
$cot\theta= -\frac{\sqrt 2}{4}$,
$sec\theta= -3$,
$csc\theta= \frac{3\sqrt 2}{4}$.
Work Step by Step
Given $cos\theta=-\frac{1}{3}$, let $x=1, r=3$, we can get $y=\sqrt {r^2-x^2}=2\sqrt 2$. Use the fact that $\theta$ is in quadrant II to determine the sign of each function, we have:
$sin\theta=\frac{y}{r}=\frac{2\sqrt 2}{3}$,
$tan\theta=-\frac{y}{x}=-2\sqrt 2$,
$cot\theta=-\frac{x}{y}=-\frac{\sqrt 2}{4}$,
$sec\theta=-\frac{r}{x}=-3$,
$csc\theta=\frac{r}{y}=\frac{3\sqrt 2}{4}$.
