Answer
$-\frac{2\sqrt 5}{5}, -\frac{\sqrt 5}{5}, 2, \frac{1}{2}, -\sqrt 5, -\frac{\sqrt {5}}{2}$
Work Step by Step
1. Given $tan\theta=2$ and $\theta$ in quadrant III, form a right triangle with sides $2,1,\sqrt {2^2+1^2}$ or $2,1,\sqrt {5}$, we have:
2. $sin\theta=-\frac{2}{\sqrt 5}=-\frac{2\sqrt 5}{5}$
3. $cos\theta=-\frac{1}{\sqrt 5}=-\frac{\sqrt 5}{5}$
4. $tan\theta=2$
5. $cot\theta=\frac{1}{tan\theta}=\frac{1}{2}$
6. $sec\theta=\frac{1}{cos\theta}=-\sqrt 5$
7. $csc\theta=\frac{1}{sin\theta}=-\frac{\sqrt {5}}{2}$
