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