Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 8 - Polar Coordinates; Vectors - Section 8.1 Polar Cordinates - 8.1 Assess Your Understanding - Page 592: 78


$ x^2+y^2=y-x$

Work Step by Step

The conversion of polar co-ordinates $(r, \theta)$ to rectangular coordinates $(x,y)$ can be expressed as: $x=r \ \cos(\theta)$, $y=r \ \sin(\theta) $ where, $r=\sqrt{x^2+y^2}$ We have: $r = \ \sin (\theta)-\cos (\theta) ~~~(1)$ Multiply equation (1) by $r$ on both sides: $r^2 = r \ \sin (\theta)-r \cos (\theta)$ Make the necessary substitutions to convert to $x,y$: $ x^2+y^2=y-x$
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.