Number of real solutions to x/100=sinx

[jason177]

I'm wondering if anyone here knows how to approach a problem like this:

The number of real solutions to the equation x/100 = sinx is...

I know I could always graph them and and count the number of intersections but that isn't really practical.

 

[Hurkyl]

I know I could always graph them and and count the number of intersections but that isn't really practical.

Try it anyways -- maybe you'll figure out a way to speed up the process along the way, or otherwise discover something useful?

 

[Werg22]

when does x/100 become greater than sin x? (hint: the answer is 100)

What happens at each successive interval of length pi/2, starting from 0?