[Math] Plotting sin(1/x)

functionsgraphing-functions

I am trying to learn how to plot sin and cos functions, and with this assingment:
$$
\sin{\frac{1}{x}}
$$

I am stuck, because I dont know how to calculate period(or is it even possible), because the period is always changing.

My question is, is it possible to calculate the period, I dont want to calculate every zero point for every period, so is it possible to calculate the rate of change of the length of the period.

Thanks.

Best Answer

It is good to note that $|f(x)|\leq1$ so it is bounded by $y=-1,~y=+1$. In fact, because of its nature, while $x$ approaches the origin, the function undergoes more and more oscillations between $+1,-1$. Also it doesn't have a limit at $x=0$. I think the rest is to find some points in $xy-$ plane and make a plot. Here, it a plot done by Maple:

enter image description here

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