Answer
$\sin$(-312.2$^{\circ}$) $\approx$ 0.74080459
Work Step by Step
$\sin$(-312$^{\circ}$ 12')
First, convert from minutes to degrees
-312$^{\circ}$ 12' = -312$^{\circ}$ + $\frac{12}{60}$
-312$^{\circ}$ $\frac{12}{60}$ = -312$^{\circ}$ + 0.2$^{\circ}$
-312$^{\circ}$ $\frac{12}{60}$ = -312.2$^{\circ}$
$\sin$(-312.2$^{\circ}$) $\approx$ 0.74080459