# What are the important points to graph y=sin (2/x)?

Dec 3, 2016

See explanation.

#### Explanation:

$y = \sin \left(\frac{2}{x}\right) \in \left[= 1 , 1\right]$

$y = 0 , x = \frac{2}{k \pi} , k = 0 , \pm 1 , \pm 2 , \ldots$

$y = 1 , x = \frac{2}{\left(2 k + \frac{1}{2}\right) \pi} , k = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$

$y = - 1 , x = \frac{2}{\left(2 k - \frac{1}{2}\right) \pi} , k = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$

The graph meets the x-axis for the last time on the right side at

$x = \frac{2}{\pi}$, and likewise, the last cut on the left is at $x = - \frac{2}{\pi}$.

The second graph reveals the decrease ( damping ) of the period of

the waves to the limit 0, as we approach x = 0.

graph{y-sin(2/x)=0 [-5, 5, -2.5, 2.5]}

graph{y-sin(2/x)=0 [-2.5, 2.5, -1.25, 1.248]}