My Math Forum area between two polar graphs

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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

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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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