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