Answer
$-\frac{\sqrt 3}{2}$,
$\frac{1}{2}$,
$-\sqrt 3$,
$-\frac{\sqrt 3}{3}$,
$2$,
$-\frac{2\sqrt 3}{3}$
Work Step by Step
Use the figure given in the exercise, we have:
1. $sin\theta=\frac{-\sqrt 3}{\sqrt {(1)^2+(-\sqrt 3)^2}}=-\frac{\sqrt 3}{2}$
2. $cos\theta=\frac{1}{\sqrt {(1)^2+(-\sqrt 3)^2}}=\frac{1}{2}$
3. $tan\theta=\frac{-\sqrt 3}{1}=-\sqrt 3$
4. $cot\theta=\frac{1}{tan\theta}=-\frac{1}{\sqrt 3}=-\frac{\sqrt 3}{3}$
5. $sec\theta=\frac{1}{cos\theta}=2$
6. $csc\theta=\frac{1}{sinn\theta}=-\frac{2}{\sqrt 3}=-\frac{2\sqrt 3}{3}$
