Explanation Given data: The given polar coordinate equation is written as follows: r = 2 − 2 cos θ Description: Condition for symmetric about the x -axis: If the point ( r , θ ) lies on a curve, then the point ( r , − θ ) or ( − r , π − θ ) also lies on the curve in order to satisfy the condition for symmetric about the x -axis. Condition for symmetric about the y -axis: If the point ( r , θ ) lies on a curve, then the point ( r , π − θ ) or ( − r , − θ ) also lies on the curve in order to satisfy the condition for symmetric about the y -axis. Condition for symmetric about the origin: If the point ( r , θ ) lies on a curve, then the point ( − r , θ ) or ( − r , θ + π ) also lies on the curve in order to satisfy the condition for symmetric about the origin. Rewrite the given polar coordinate equation as follows: r = 2 − 2 cos θ (1) Substitute ( r , θ ) in the Equation (1) as follows: r = 2 − 2 cos θ (2) Substitute ( r , − θ ) in the Equation (1) as follows: r = 2 − 2 cos (

Thomas' Calculus: Early Transcendentals (14th Edition)

14th Edition

ISBN: 9780134439020

Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher: PEARSON

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Chapter 11.4, Problem 2E

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Identify the symmetry of the given curve and sketch the curve in the xy-plane.

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Chapter 11 Solutions

Thomas' Calculus: Early Transcendentals (14th Edition)

Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Finding Cartesian from Parametric...Ch. 11.1 - Finding Cartesian from Parametric...

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Identify the symmetry of the given curve and sketch the curve in the xy -plane.

Identify the symmetry of the given curve and sketch the curve in the xy-plane.

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Chapter 11 Solutions