Answer
The domain $D$ consists of all points $\left( {x,y} \right)$ with $x=0$ excluded:
$D = \left\{ {\left( {x,y} \right)|x \ne 0} \right\}$
Work Step by Step
The function $f\left( {x,y} \right) = \sin \frac{y}{x}$ is defined only when $x \ne 0$. Thus, the domain $D$ consists of all points $\left( {x,y} \right)$ with $x=0$ excluded:
$D = \left\{ {\left( {x,y} \right)|x \ne 0} \right\}$
