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 $\theta=-1290^\circ=-3\times360^\circ-210^\circ$ (quadrant II, reference angle $30^\circ$), 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 $csc\theta = \frac{1}{sin\theta}=2$.
