Answer
$\cot$(-512$^{\circ}$ 20') $\approx$ 1.90714493
Work Step by Step
$\cot$(-512$^{\circ}$ 20')
First, convert from minutes to degrees
-512$^{\circ}$ 20' = -512$^{\circ}$ + $\frac{20}{60}$
-512$^{\circ}$ $\frac{20}{60}$ = -512$^{\circ}$ + 0.33$^{\circ}$
-312$^{\circ}$ $\frac{20}{60}$ = -512.33$^{\circ}$
$cot$(-512.33$^{\circ}$) $\approx$ 1.90714493
Therefore:
$\cot$(-512$^{\circ}$ 20') $\approx$ 1.90714493