Number of real solutions to x/100=sinx

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The discussion focuses on finding the number of real solutions to the equation x/100 = sin(x). Participants suggest that while graphing the functions is one approach, it may not be the most efficient method. A key point raised is to consider when x/100 exceeds sin(x), which occurs at x = 100. Additionally, examining the behavior of the functions at intervals of length π/2 from 0 is recommended for further insights. Understanding these intervals can help in determining the number of intersections and solutions.
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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.
 
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jason177 said:
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?
 
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?
 
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