cbicon.png CALCULUS Understanding Its Concepts and Methods

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Rectangular coordinates

To describe points in a plane, we draw two axes: a horizontal one called the x-axis and a vertical one called the y-axis.
graphics/IE_coordinates__4.png
Given a point P = (a, b), the number  a is called the  x-coordinate and b is the y-coordinate.

To describe objects in space, we need three axes. These are usually labeled x, y, and z, reading counterclockwise as you face the origin from the positive sides of all three the axes. This is sometimes described as the right-hand rule: If you curl the fingers of your right hand about the z-axis in a direction that rotates from the x-axis to the y-axis in a counterclockwise direction, your thumb will point in the direction of the positive z-axis.

x
y
z
Point (x, y, z)
Point (x, y, z)
Point (x, y, z)
- axa
x = a
x = a
y = b
- byb
y = b
z = c
z = c
- czc

Given a point P = (a, b, c), the number a is called the x-coordinate, b is the y-coordinate, and c is the z-coordinate.


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

Polar coordinates

Spherical 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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