Answer
$\frac{5\sqrt {26}}{26}, -\frac{\sqrt {26}}{26}, -5, -\frac{1}{5}, -\sqrt {26}, \frac{\sqrt {26}}{5}$
Work Step by Step
1. Graph $y=-5x, x\leq0$ and the least positive angle $\theta$ as shown. We can identify a point $(-1,5)$ on the line.
2. $sin\theta=\frac{5}{\sqrt {(-1)^2+(5)^2}}=\frac{5}{\sqrt {26}}=\frac{5\sqrt {26}}{26}$
3. $cos\theta=\frac{-1}{\sqrt {(-1)^2+(5)^2}}=\frac{-1}{\sqrt {26}}=-\frac{\sqrt {26}}{26}$
4. $tan\theta=\frac{5}{-1}=-5$
5. $cot\theta=\frac{1}{tan\theta}=-\frac{1}{5}$
6. $sec\theta=\frac{1}{cos\theta}=-\sqrt {26}$
7. $csc\theta=\frac{1}{sin\theta}=\frac{\sqrt {26}}{5}$
