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Area inside two polar curves

  1. May 13, 2006 #1

    G01

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    I need to find the area thats inside both of the following curves:

    [tex] r = \sin\theta [/tex]

    [tex] r = \cos\theta [/tex]

    I know that I should have to subtract the area of the one curve from the other and I know the area formula for polar coordinates, but I just can't see how to set this one up any help or hints would be appreciated.
     
  2. jcsd
  3. May 13, 2006 #2
    It's just two circles. the sin one is centered on the y axis and the cos one is centered on the x axis. Sketch them and you will see what you have to do. Because of symmetry, you only need to integrate sin(t) from t=0 to t=pi/4 and multiply that integral by 2. Integrating cos(t) from t=pi/4 to t=pi/2 and then multiplying that integral by 2 will give you the same exact result.
     
  4. May 13, 2006 #3

    G01

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    Shouldn't the area of sin t from 0 to pi/4 cover everything from the curve to the y axis. If you multiply that by 2 then you will end up with more area than whats in the loop won't you? I'm sorry I must be really confused
     
  5. May 13, 2006 #4
    No, thats 0 to pi/2. pi/4 is 1/8th of a circle
     
  6. May 13, 2006 #5

    G01

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    these circles complete one rotation every pi degrees remember. So Pi/4 would be at the top of the circle with the cos and at the side of the sine circle.
     
  7. May 13, 2006 #6
    Dude, why are you arguing with me? I said that you integrate sin(t) from 0 to pi/4. If you don't think my answer is right, then don't use it.
     
  8. May 14, 2006 #7

    G01

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    Im sorry, I think my explaination of this problem was bad I'm going to try to explain it again in another thread so I you still feel like halping me please go there.
     
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