Example 4. Determine the non-negative roots of the equation $\sin x=\frac{1}{100} x$
The roots of the equation are the x-coordinates of the intersection points of the graphs of $y=\sin x$ and $y=\frac{1}{100} x$. Therefore, we only need to find the number of intersection points of the two functions in the first quadrant. This can be solved by observing the graphs.
Solution: The curve $y=\sin x$ and the line $y=\frac{1}{100} x$

intersect in the first quadrant within the rectangle bounded by the lines $x=0, x=100$, $y=0, y=1$.
Since $31 \pi < 100 < 32 \pi$, the interval $[0,100]$ can be divided into 32 subintervals: $[0, \pi], [\pi, 2 \pi], \cdots, [30 \pi, 31 \pi], [31 \pi, 100]$. We can construct 32 rectangles using these intervals as their bases.
Furthermore, the intersection points of the line $y=\frac{1}{100} x$ and the curve $y=\sin x$ are only within the 1st, 3rd, ..., 31st rectangles, and each rectangle has only two intersection points. Therefore, the equation has 32 non-negative roots.
From the above, the observations made from the graphs serve as a "guide" for finding the solution. However, only by being imaginative based on these observations can one open the floodgates of thinking.