It is the set $V(y-\sin(x))\subset k^2$ a variety? It is the set $V(y-\sin(x))\subset k^2$ a variety?
I know that $V(y-\sin(x))=\{...,-4\pi,-3\pi,-2\pi,-\pi,0,\pi,2\pi,3\pi,4\pi,...\}$. Could it be a set of points a variety? My intuition tells me what not. How can I do a formal test, what property should I use? Thank you very much.

$V=V(y-\sin(x))=\{(x,y); y=\sin(x) \}=\{(x,\sin(x)); x\in \Bbb R \}$  is not variety because no polynomial in $\Bbb R[x,y]$ has zeroes the set $V$.
