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The graph of \(r = \cos 3 \theta\) is shown below. 

If we plot the graph of \(r = \cos 3 \theta\) for \(0 \le \theta \le M\), then what is the smallest value of M that still produces the entire graph of \(r = \cos 3 \theta\)?

 Dec 15, 2019
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We need the radius to come back to the origin.  The smallest M that makes r = 0 is 2*pi/3.

 Dec 16, 2019

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