Answer
$F$ is a conservative vector field with potential function $f(x,y)=xsiny+cosz+C$
Work Step by Step
Given: $F(x,y,z)=sinyi+xcosyj-sinzk$
$F=Pi+Qj+Rk$ will be conservative when $R_y=Q_z$,$P_y=Q_x$, and $P_z=R_x$
$F$ is a conservative vector field with potential function $f(x,y)=xsiny+cosz+C$
