Answer
$tan\theta= -\frac{\sqrt 2}{4}$,
$cot\theta= -2\sqrt 2$,
$sec\theta= \frac{3\sqrt 2}{4}$,
$csc\theta= -3$.
Work Step by Step
Given $sin\theta=-\frac{1}{3}, cos\theta=\frac{2\sqrt 2}{3}$, we have:
$tan\theta=\frac{sin\theta}{cos\theta}=-\frac{\sqrt 2}{4}$,
$cot\theta=\frac{cos\theta}{sin\theta}=-2\sqrt 2$,
$sec\theta=\frac{1}{cos\theta}=\frac{3\sqrt 2}{4}$,
$csc\theta=\frac{1}{sin\theta}=-3$.
