Explanation Use Cartesian-to-polar method to draw the graph for r = sin 2 ( θ 2 ) . Step 1: Draw the graph of r = sin 2 ( θ 2 ) in Cartesian coordinate system by taking θ on the horizontal axis and r on the vertical axis. Select the interval [ 0 , 2 π ] as the sine function is 2 π periodic function. First draw the graph of r = sin 2 ( θ 2 ) over the interval [ 0 , 2 π ] in the Cartesian coordinate system as shown below in Figure 1. From Figure 1, observe that the curve initiates from r = 0 when θ = 0 then it reaches to r = 0.5 when θ = π 2 then r takes the value 1 again for θ = π and reaches to r = 0

Calculus, Single Variable: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134766850

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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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 12.2, Problem 59E

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To draw: Thepolar curve for r=sin2(θ2) and verify the graph by using graphing utility.

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Chapter 12.2, Problem 58E

Chapter 12.2, Problem 60E

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Chapter 12 Solutions

Calculus, Single Variable: Early Transcendentals (3rd Edition)

Ch. 12.1 - Identify the graph generated by the parametric...Ch. 12.1 - Prob. 2QC Ch. 12.1 - Prob. 3QC Ch. 12.1 - Prob. 4QC Ch. 12.1 - Prob. 5QC Ch. 12.1 - Prob. 6QC Ch. 12.1 - Explain how a pair of parametric equations...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E

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To draw: Thepolar curve for r = sin 2 ( θ 2 ) and verify the graph by using graphing utility.

Solution Summary: The author explains how to draw the polar curve for r=mathrmsin2(theta

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To draw: Thepolar curve for r=sin2(θ2) and verify the graph by using graphing utility.

Want to see the full answer?

Chapter 12 Solutions