Answer
$-\frac{5\sqrt {26}}{26}, \frac{\sqrt {26}}{26}, -5, -\frac{1}{5}, \sqrt {26}, -\frac{\sqrt {26}}{5}$
Work Step by Step
Given point $(1,-5)$ on the terminal side, we have:
1. $sin\theta=\frac{-5}{\sqrt {(1)^2+(-5)^2}}=-\frac{5}{\sqrt {26}}=-\frac{5\sqrt {26}}{26}$
2. $cos\theta=\frac{1}{\sqrt {(1)^2+(-5)^2}}=\frac{1}{\sqrt {26}}=\frac{\sqrt {26}}{26}$
3. $tan\theta=\frac{-5}{1}=-5$
4. $cot\theta=\frac{1}{tan\theta}=-\frac{1}{5}$
5. $sec\theta=\frac{1}{cos\theta}=\sqrt {26}$
6. $csc\theta=\frac{1}{sin\theta}=-\frac{\sqrt {26}}{5}$
