Answer
To convert a rectangular equation in x and y to a polar equation in r and $\theta $, replace $x$ with $r\cos \theta $ and $y$ with $r\sin \theta $.
Work Step by Step
The variables of a polar equation are r and $\theta $. To convert a rectangular equation represented in x and y to a polar equation represented in r and $\theta $, we will replace $x$ with $r\cos \theta $ and $y$ with $r\sin \theta $.
For example, consider a rectangular equation $x+y=7$. To convert it into a polar equation, we will replace $x$ with $r\cos \theta $ and $y$ with $r\sin \theta $. Therefore,
$\begin{align}
& r\cos \theta +r\sin \theta =7 \\
& r\left( \cos \theta +\sin \theta \right)=7 \\
& r=\frac{7}{\cos \theta +\sin \theta }
\end{align}$
Hence, the polar equation of the form $x+y=7$ is $r=\frac{7}{\cos \theta +\sin \theta }$.
