Area of polars help! find the area between the outer and inner loops of r = 1 + 2cos3(theta)

[alyh]

I'm supposed to find the area between the outer loops and the inner loops of r=1+2cos3(theta), but I do not understand the bounds for big loops and the bounds for the little loops. I understand how to find them (setting r equal to 0), but why those the bounds for each region, if that makes sense?

I appreciate the help!!

This is my teacher's answer key, for reference:

 

[Dr.Peterson]

I'm supposed to find the area between the outer loops and the inner loops of r=1+2cos3(theta), but I do not understand the bounds for big loops and the bounds for the little loops. I understand how to find them (setting r equal to 0), but why those the bounds for each region, if that makes sense?

I appreciate the help!!

This is my teacher's answer key, for reference:
View attachment 37286

Did you try sketching the graph, by observing how r varies when theta goes from 0 to 4pi/9?