Explanation Given: The rectangular equation is x 2 + y 2 − 4 x = 0 . Formula used: For converting rectangular to polar coordinate system , tan θ = y x r 2 = x 2 + y 2 The zero factor property that is when A B = 0 , then A = 0 or B = 0 , where A and B are algebraic expressions. Calculation: Consider the rectangular equation x 2 + y 2 − 4 x = 0 . Recall that for converting rectangular to polar coordinate system, tan θ = y x r 2 = x 2 + y 2 Also, x = r cos θ y = r sin θ Substitute r cos θ for x and r sin θ for y . ( r cos θ ) 2 + ( r sin θ ) 2 − 4 ( r cos θ ) = 0 r 2 cos 2 θ + r 2 sin θ − 4 r cos θ = 0 Take the common terms out from left hand side. r 2 cos 2 θ + r 2 sin θ − 4 r cos θ = 0 r 2 ( cos 2 θ + sin θ ) − 4 r cos θ = 0 Use the identity, cos 2 θ + sin 2 θ = 1 r 2 ( 1 ) − 4 r cos θ = 0 r 2 − 4 r cos θ = 0 Take the common terms out from left hand side. r 2 − 4 r cos θ = 0 r ( r − 4 cos θ ) = 0 Recall the zero factor property that is when A B = 0 , then A = 0 or B = 0 , where A and B are polar expressions. So, either r = 0 or r − 4 cos θ = 0

10th Edition

ISBN: 9781285057095

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 10, Problem 72RE

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To calculate: The polar form of the rectangular equation x2+y2−4x=0 and sketch its graph.

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Chapter 10, Problem 71RE

Chapter 10, Problem 73RE

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Chapter 10 Solutions

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The polar form of the rectangular equation x 2 + y 2 − 4 x = 0 and sketch its graph.

Solution Summary: The author calculates the polar form of the rectangular equation x2+y4x=0 and sketched its graph.

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Chapter 10 Solutions