Answer
$-\frac{1}{2}$, $ -\frac{\sqrt 3}{2}$, $ \frac{\sqrt 3}{3}$, $ \sqrt 3$, $ -\frac{2\sqrt 3}{3}$, and $ -2$.
Work Step by Step
Given $\theta=570^\circ=360^\circ+210^\circ=360^\circ+180^\circ+30^\circ$ (quadrant III), we have $sin\theta =-sin30^\circ=-\frac{1}{2}$, $cos\theta =-cos30^\circ=-\frac{\sqrt 3}{2}$, $tan\theta =tan30^\circ=\frac{\sqrt 3}{3}$, $cot\theta = \frac{1}{tan\theta}=\sqrt 3$, $sec\theta = \frac{1}{cos\theta}=-\frac{2\sqrt 3}{3}$, and $csc\theta = \frac{1}{sin\theta}=-2$.
