Complete curves Consider the polar curve r = cos (n/m),

Chapter 8, Problem 106AE

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QUESTION:

Consider the polar curve \(r=\cos\ (n\theta/m)\), where n and m are integers.

a. Graph the complete curve when n = 2 and m = 3.

b. Graph the complete curve when n = 3 and m = 7.

c. Find a general rule in terms of m and n for determining the least positive number P such that the complete curve is generated over the interval [0, P].

Questions & Answers

QUESTION:

Consider the polar curve \(r=\cos\ (n\theta/m)\), where n and m are integers.

a. Graph the complete curve when n = 2 and m = 3.

b. Graph the complete curve when n = 3 and m = 7.

c. Find a general rule in terms of m and n for determining the least positive number P such that the complete curve is generated over the interval [0, P].

ANSWER:

Solution 106AEStep 1:Given: a. Using n = 2 and m = 3, we get Graph of is: b. Using n = 3

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