Answer
$sin\theta=-\frac{7}{25}$, $cos\theta=-\frac{24}{25}$, $tan\theta=\frac{7}{24}$, $sec\theta=-\frac{25}{24}$, $csc\theta=-\frac{25}{7}$
Work Step by Step
1. Given $cot\theta=\frac{24}{7}$ and $cos\theta\lt0$, we have $tan\theta=\frac{1}{cot\theta}=\frac{7}{24}$ and $\theta$ in quadrant III.
2. Let $x=-24, y=-7$, we have $r=\sqrt {x^2+y^2}=25$
3. We can find:
$sin\theta=-\frac{7}{25}$,
$cos\theta=-\frac{24}{25}$,
$tan\theta=\frac{7}{24}$,
$sec\theta=-\frac{25}{24}$,
$csc\theta=-\frac{25}{7}$
