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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 \(S\).

 Nov 15, 2019
 #1
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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

 

 

cool cool cool

 Nov 15, 2019

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