Roots of sin in algebra? please help!!!

Roots of sin in algebra? please help!!!



How would I go about creating a function that has the number of roots of this function since the origin on the x-axis and the distance between that root and the last/next(I'm not sure which would be easier to do) on the y-axis.

So, for example:
the y-value of the x-coordinate 5 will be the distance between the 4th and 5th root of this function.

I have another question too, you don't have to answer both, but what information would an integral of such a function provide?

I hope I'm not too confusing, or that this is really obvious and I just couldn't figure it out





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