Explanation Given: { r = 3 θ θ = π 3 Calculation: Consider the polar curves for 0 ≤ θ ≤ 5 π . r = 3 θ θ = π 3 Sketch the graph: From the sketch it is obvious that ( 0 , 0 ) is the point of intersection. The line θ = π 3 will intersect the curve two times while the curve will be rotated one time between the intervals 0 ≤ θ ≤ 2 π , 2 π ≤ θ ≤ 4 π , 4 π ≤ θ ≤ 6 π and so on. On the upper half, the point of intersection is r = ( 3 n + 1 ) π , n even, θ = π 3 . On the bottom half, the point of intersection is r = ( 3 n + 1 ) π , n odd, θ = π , π 3

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 6.3, Problem 25PS

To determine

To find: the points of intersection of the curves.

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Chapter 6.3, Problem 24PS

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Chapter 6 Solutions

Calculus

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the points of intersection of the curves.

Solution Summary: The author illustrates the point of intersection of the polar curves by drawing the graph.

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Chapter 6 Solutions