How many solutions has the equation $\sin x= \frac{x}{100}$ ? How many solutions has the equation $\sin x= \frac{x}{100}$ ? 
Usually when I was asked to solve this type of problem, I would solve it graphically but this one seems to be trickier. It doesn't seem wise to put $f(x)=\sin x$ and $g(x)=\frac{x}{100}$ in the same graph and then counting all the intersection points. 
What would be some algebraic methods to solve this? 

Outside of the interval $[-100, 100]$ there are no solutions.
$x = 100\;$ occurs close to the right end of the interval $[30 \pi, 32 \pi]$
$x = -100\;$ occurs close to the left end of the interval $[-32 \pi, -30 \pi]$
Each interval $[2n\pi, (2n+2)\pi]$ will have 2 solutions for $n = -32$ to $n = 30$ except $x = 0$ will get counted twice.
So there are $2*32-1 = 63\;$ solutions.
