## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 6 - Section 6.3 - Polar Coordinates - Exercise Set - Page 744: 93

#### 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 $r=\frac{7}{\cos \theta +\sin \theta }$.

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