This is equivalent to count the intersection points of line $y=\frac{x}{2018}$ and the plot $y=\sin x$. As shown in the graph below, including $0$, there are two intersection points in $[0, \pi]$, two in $[2\pi, 3\pi]$, etc, on the positive $x$ side. This means there are two intersection points in every $2\pi$ interval. When the straight line $y=\frac{x}{2018}$ goes beyond $y=1$ (correspondingly, $x=2018$), there will be no more intersection point.

Because $2018\div (2\pi)\approx 321.17$, there will be $321$ whole $2\pi$ waves. This means there will be $321\times 2 = 642$ points. The additional $0.17$ wave will not intersect the line $y=\frac{x}{2018}$ because the line will be very close to the line $y=1$ but $0.17$ wave will not reach that high. The number of intersection points on the negative side is exactly the same as that on the positive side. However, the point $0$ is double counted. Therefore, the final answer is $642\times 2 -1 = \boxed{1283}$.