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: 79

Answer

$ x^2+y^2= 4$

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: $r = 2 \ ~~~(1)$ Squaring both sides of equation (1), we have: $r^2 = 4$ Make the necessary substitutions to convert to $x,y$: Therefore, $ x^2+y^2= 4$
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