Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 6 - Section 6.3 - Polar Coordinates - Exercise Set - Page 743: 54



Work Step by Step

Rectangular equation is ${{x}^{2}}+{{y}^{2}}=16$ …… (I) The relation between polar coordinates and rectangular coordinates can be expressed as below: $x=r\cos \theta \ \text{ and }\ y=r\sin \theta $ …… (II) Substitute values of $x\ \text{ and }\ y$ from (II) in (I), to get $\begin{align} & {{x}^{2}}+{{y}^{2}}=16 \\ & {{\left( r\cos \theta \right)}^{2}}+{{\left( r\sin \theta \right)}^{2}}=16 \\ & {{r}^{2}}\left( {{\cos }^{2}}\theta +{{\sin }^{2}}\theta \right)=16 \end{align}$ As, $\left( {{\cos }^{2}}\theta +{{\sin }^{2}}\theta \right)=1$ From here we get, $\begin{align} & {{r}^{2}}=16 \\ & r=4 \end{align}$ Hence the obtained polar expression is $r=4$.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.