Answer
$\sin\theta=\frac{2\sqrt 6}{7}$,
$\cot\theta-\frac{5\sqrt 6}{12}$,
$\sec\theta=-\frac{7}{5}$,
$\csc\theta=\frac{7\sqrt 6}{12}$
Work Step by Step
1. Given $tan\theta=-\frac{2\sqrt 6}{5}\lt0$ and $cos\theta=-\frac{5}{7}\lt0$, we can identify $\theta$ to be in quadrant II.
2. Let $x=-5, y=2\sqrt 6, r=7$, we have:
$sin\theta=\frac{2\sqrt 6}{7}$,
$cot\theta=-\frac{5}{2\sqrt 6}=-\frac{5\sqrt 6}{12}$,
$sec\theta=-\frac{7}{5}$,
$csc\theta=\frac{7}{2\sqrt 6}=\frac{7\sqrt 6}{12}$
