To determine Identify the appropriate equation for the given Four-leaved rose from the given equations. Explanation Calculation: From the given Four-leaved rose, it is clear that, the graph is symmetrical to both x - and y -axes, but, it is not symmetrical to the origin. Therefore, the probable equation for four leaved rose is r = sin ( 2 θ ) . Verify whether the polar equation r = sin ( 2 θ ) satisfy the symmetrical status of four leaved rose or not as follows: 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 probable polar coordinate equation as follows: r = sin ( 2 θ ) (1) Substitute ( r , θ ) in the Equation (1) as follows: r = sin ( 2 θ ) (2) Substitute ( − r , π − θ ) in the Equation (1) as follows: − r = sin 2 ( π − θ ) = sin ( 2 π − 2 θ ) = − si

Student Solutions Manual For Thomas' Calculus Format: Paperback

14th Edition

ISBN: 9780134439334

Author: Hass, Joel R.^heil, Christopher D.^weir, Maurice D.^heil, Christopher

Publisher: PEARSON

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Chapter 11, Problem 39PE

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Identify the appropriate equation for the given Four-leaved rose from the given equations.

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Chapter 11, Problem 38PE

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Student Solutions Manual For Thomas' Calculus Format: Paperback

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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