Question

What is the best answer for sin(\dfrac{2}{x})=0

Answer 1

The sine of an angle is zero if and only if the angle is zero, with a periodicity of $\pi$

In other words, you have

$\sin(\alpha)=0\iff\alpha=0,\ \pm\pi,\ \pm 2\pi\ldots = k\pi,\ k\in\mathbb{Z}$

So, we have

$\sin\left(\dfrac{2}{x}\right)=0 \iff \dfrac{2}{x}=k\pi \iff x =\dfrac{2}{k\pi}$