Mathematics

Problem

![A polar coordinate graph showing the intersection of two curves. The outer curve is a circle of radius 2 (r=2). The inner curve is a rose curve (r=2cos(3\theta)). The shaded regions are the areas inside the circle but outside the rose curve, located in the first and third quadrants.](https://storage.googleapis.com/diraq-contents/homework-question-parsing/marker/20260110T055645Z/c409b36beee64af1930066637067d0e8/a2b0b8d868ec4ee43d7d3f0961a12b5e_img.jpg) The figure above shows the graphs of the polar curves

r = 2\cos(3\theta)

and

r = 2

. What is the sum of the areas of the shaded regions?

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