how to draw sin(1/x)?

thanks.

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- Nov 28th 2010, 03:53 AMBabyMilohow to draw sin(1/x)
how to draw sin(1/x)?

thanks. - Nov 28th 2010, 04:00 AMarccos
Note that the period is 1/360.(correct me if im wrong) As it seems to me,it would squeeze towards the origin.

- Nov 28th 2010, 04:07 AMe^(i*pi)
- Nov 28th 2010, 04:10 AMBabyMilo
- Nov 28th 2010, 04:12 AMarccos
Ah that's interesting. I'm curious to know why it started to open up. My guess is that when x = 1 it will start to widen. As with eg. sin(x/2) = 720 degree period.

- Nov 28th 2010, 04:49 AMArchie Meade
Start with $\displaystyle sin(n{\pi})=0,\;\;\;n=0,\;1,\;2,\;3......$

$\displaystyle \displaystyle\ sin\left[\frac{(4n+1){\pi}}{2}\right]=1$

$\displaystyle \displaystyle\ sin\left[\frac{(4n+3){\pi}}{2}\right]=-1$

Then if

$\displaystyle \displaystyle\ sin(n{\pi})=0\Rightarrow\ n{\pi}=\frac{1}{x}\Rightarrow\ x=\frac{1}{n{\pi}}$

shows that the graph crosses the x-axis at

$\displaystyle \displaystyle\ x=\frac{1}{\pi},\;\;\frac{1}{2{\pi}},\;\;\frac{1}{ 3{\pi}},\;\;,\frac{1}{4{\pi}},.....$

an "infinite" number of times approaching x=0.

The function is non-periodic and approaches 0 as x approaches $\displaystyle \infty$ - Nov 28th 2010, 04:59 AMBabyMilo
- Nov 28th 2010, 05:08 AMArchie Meade