Answer
$tan\theta= \frac{1}{2}$,
$cot\theta= 2$,
$sec\theta= -\frac{\sqrt 5}{2}$,
$csc\theta= -\sqrt 5$.
Work Step by Step
Given $sin\theta=-\frac{\sqrt 5}{5}, cos\theta=-\frac{2\sqrt 5}{5}$, we have:
$tan\theta=\frac{sin\theta}{cos\theta}=\frac{1}{2}$,
$cot\theta=\frac{cos\theta}{sin\theta}=2$,
$sec\theta=\frac{1}{cos\theta}=-\frac{\sqrt 5}{2}$,
$csc\theta=\frac{1}{sin\theta}=-\sqrt 5$.
