Answer
$cot[arctan(-\frac{3}{5})]=-\frac{5}{3}$
Work Step by Step
Let $u=arctan(-\frac{3}{5})$. Then:
$tan~u=-\frac{3}{5}$
The range $arctan~x$ is $-\frac{\pi}{2}\lt x\lt\frac{\pi}{2}$. So, since $arctan(-\frac{3}{5})\lt0$, then $-\frac{\pi}{2}\lt u\lt0~~$ (Fourth Quadrant)
$cot[arctan(-\frac{3}{5})]=cot~u=\frac{1}{tan~u}=-\frac{5}{3}$
