jmc

For each point on the unit circle with $y$-coordinate equal to $-0.73$, there is a corresponding angle whose sine is $-0.73$. There are two such points; these are the intersections of the unit circle and the line $y=-0.73$, shown in red above. Therefore, there are $\boxed{2}$ values of $x$ with $0^{\circ }\le x<360^{\circ }$ such that $\sin x=-0.73$.