Answer
In converting $r=\sin \theta $ from a polar equation to a rectangular equation, multiply both sides of the equation by r so that the left hand side becomes ${{r}^{2}}$, which gets replaced with ${{x}^{2}}+{{y}^{2}}$ and the right hand side becomes $r\sin \theta$, which gets replaced with $y$.
Work Step by Step
Consider the given polar equation, $r=\sin \theta $
Multiplying both sides of the equation by r, we get,
${{r}^{2}}=r\sin \theta $
Use, ${{r}^{2}}={{x}^{2}}+{{y}^{2}}$ and $y=r\sin \theta $
Therefore,
${{x}^{2}}+{{y}^{2}}=y$
Hence, to convert $r=\sin \theta $ from the polar equation to a rectangular equation we will multiply both sides of the equation by r, so that the left hand side becomes ${{r}^{2}}$ which gets replaced with ${{x}^{2}}+{{y}^{2}}$ and the right hand side becomes $r\sin \theta $ which gets replaced with $y$.
