Why is the graph y=sin(x/y) so grainy/messy?

Question

I was just plotting random functions, and observed that the graph of y=sin(x/y) looks like randomly scattered grains or threads along the x axis! Same goes with sin(y/x). So what is going on with the function there? Is it just a rendering issue?

Answer 1

For every $0<|y|\le 1$ there are many solutions $x$: $$ \frac{x}{y}= \begin{cases} \arcsin y+2\pi k,\\ \pi-\arcsin y+2\pi k\\ \end{cases}\quad\Leftrightarrow\quad x=\begin{cases} y\arcsin y+2\pi k y,\\ -y\arcsin y+(\pi+2\pi k) y\\ \end{cases} $$ Try to plot the dependence $x=x(y)$ for $k=0,\pm 1,\pm 2$ to see what happens and then switch the axes.