## Precalculus (6th Edition) Blitzer

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 $y$.
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 $y$.