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November 21st, 2016, 02:57 AM  #1 
Newbie Joined: Nov 2016 From: Poland Posts: 1 Thanks: 0  area between two polar graphs
How to find the area of two polar graphs if r=4sin theta and 10cos theta?

November 21st, 2016, 05:01 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,942 Thanks: 1546 
I assume you mean the area enclosed between the two polar graphs, correct? Start by sketching their respective graphs (both are circles). Sketch shows an intersection point at the pole and in quadrant I. Find the point of intersection in quad I ... $10\cos{t}=4\sin{t} \implies \tan{t}=\dfrac{5}{2} \implies t = \arctan\left(\dfrac{5}{2}\right)$ Let $\phi = \arctan\left(\dfrac{5}{2}\right)$ ... $\displaystyle A= \int_0^\phi \dfrac{(4\sin{t})^2}{2} \, dt + \int_\phi^{\pi/2} \dfrac{(10\cos{t})^2}{2} \, dt$ can you finish? 

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area, graphs, polar 
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