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Polar coordinates

The polar coordinates of a point $P$ in the plane are its distance $r$ from the origin $O$ and the angle $\alpha $ that the line segment MATH makes with the positive $x$-axis.

The angle $\alpha $ is positive if it is measured counter-clockwise from the positive $x$-axis, and negative if it is measured clockwise from the positive $x$-axis. The point $(-r,\alpha )$ is identified with the point $(r,\alpha +\pi )$.

graphics/IE_polar__14.png
$\alpha $ positive
graphics/IE_polar__16.png
$\alpha $ negative



A B C D E F G H I J K L M N O P Q R S T U V W X Y Z


Cylindrical coordinates

Double integral in polar coordinates


Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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