Let \(S\) be the set of points with polar coordinates \((r,\theta)\) such that \( 2 \le r \le 6\)and \(\frac{\pi}{3} \le \theta \le \frac{5 \pi}{6}\). Find the area of \(S\).
pi/3 = 60°
5pi/6 = 150°
150 - 60 = 90°
So....this is just the area between a quarter-circle with a radius of 6 and a quarter-circle with a radius of 2
So S =
(pi/4) [ 6^2 - 2^2 ] =
(pi /4 ) [ 32] =
8 pi units^2
