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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 4, 2018
 #1
avatar+94545 
+3

Note......

 

When θ = 0     r = 3

When θ = pi / 6, r = 0

 

And this traces out   (1/2) of a "leaf"

So....each pi/6 rads will do the same

So.....6 of these will trace out 3 full "leaves"

 

So

 

6 (pi/6)  =   pi  =    M   =   (180”)

 

 

cool cool cool

 Dec 4, 2018

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