Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 10 - Conics, Parametric Equations, and Polar Coordinates - 10.4 Exercises - Page 722: 12

Answer

\[\left( {6,\frac{{3\pi }}{2}} \right),\left( { - 6,\frac{\pi }{2}} \right)\]

Work Step by Step

$$\eqalign{ & {\text{We have the rectangular coordinates }}\left( {x,y} \right) = \left( {0, - 6} \right) \cr & {\text{The polar coordinates are:}} \cr & r = \sqrt {{x^2} + {y^2}} \cr & r = \sqrt {{{\left( 0 \right)}^2} + {{\left( { - 6} \right)}^2}} \cr & r = 6 \cr & \tan \theta = \frac{{ - 6}}{0} \cr & \theta = {\tan ^{ - 1}}\left( {\frac{{ - 6}}{0}} \right) \cr & \theta = \frac{{3\pi }}{2},{\text{ }}\theta = \frac{\pi }{2} \cr & {\text{Therefore, the polar coordinates are:}} \cr & \left( {r,\theta } \right) = \left( {6,\frac{{3\pi }}{2}} \right),\left( { - 6,\frac{\pi }{2}} \right) \cr} $$
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.