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

4th Edition

ISBN: 9780134439099

Author: Hass, Joel., Heil, Christopher , WEIR, Maurice D.

Publisher: Pearson,

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Chapter 11.4, Problem 1E

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

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Chapter 11.3, Problem 68E

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Chapter 11 Solutions

Thomas' Calculus

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 - Prob. 9E 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