Plotting sin(1/x)

Question

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.

Answer 1

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:

Answer 2

Since near $x=0$ the function goes wild, you can't hope that it is periodic... Take the sequences $a_n=\frac{1}{\pi/2+2\pi k}, b_n=\frac{1}{3\pi/2+2\pi k}$ and watch what happens.

For plotting graphs, it is always useful to consult W|A: http://www.wolframalpha.com/input/?i=plot+sin%281%2Fx%29 .