Precalculus (6th Edition) Blitzer

The polar equation of ${{x}^{2}}+{{y}^{2}}=9$ which express $r$ in terms of $\theta$ is $r=3$.
The relation between polar coordinates and rectangular coordinates can be represented as below: $x=r\cos \theta \ \text{ and }\ y=r\sin \theta$ …… (2) Substitute the values of $x\ \text{ and }\ y$ from (2) in (1) to get, \begin{align} & {{x}^{2}}+{{y}^{2}}=9 \\ & {{\left( r\cos \theta \right)}^{2}}+{{\left( r\sin \theta \right)}^{2}}=9 \\ & {{r}^{2}}\left( {{\cos }^{2}}\theta +{{\sin }^{2}}\theta \right)=9 \end{align} As, $\left( {{\cos }^{2}}\theta +{{\sin }^{2}}\theta \right)=1$ From here we get, \begin{align} & {{r}^{2}}=9 \\ & r=3 \end{align}