Answer
0.740805
Work Step by Step
Converting $-312^{\circ}12'$ to decimal degrees, we get
$-312^{\circ}12'=-(312^{\circ}+\frac{12}{60}^{\circ})=-(312^{\circ}+0.2^{\circ})=-312.2^{\circ}$
$\sin(-312^{\circ}12')=\sin(-312.2^{\circ})\approx0.740805$
