Answer
$-\frac{2}{5}, -\frac{\sqrt {21}}{5}, \frac{2\sqrt {21}}{21}, \frac{\sqrt {21}}{2}, -\frac{5\sqrt {21}}{21}, -\frac{5}{2}$
Work Step by Step
1. Given $sin\theta=-\frac{2}{5}$ and $\theta$ in quadrant III, form a right triangle with sides $2,\sqrt {5^2-2^2},5$ or $2,\sqrt {21},5$, we have:
2. $sin\theta=-\frac{2}{5}$
3. $cos\theta=-\frac{\sqrt {21}}{5}$
4. $tan\theta=\frac{2}{\sqrt {21}}=\frac{2\sqrt {21}}{21}$
5. $cot\theta=\frac{1}{tan\theta}=\frac{\sqrt {21}}{2}$
6. $sec\theta=\frac{1}{cos\theta}=-\frac{5\sqrt {21}}{21}$
7. $csc\theta=\frac{1}{sin\theta}=-\frac{5}{2}$
