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Area in Polar Coordinates

  1. Oct 18, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the area of the region bounded by r=8cos10[tex]\Theta[/tex]

    2. Relevant equations

    3. The attempt at a solution

    I set r=0 to find [tex]\Theta[/tex], which i used for my bounds
    [tex]\Theta[/tex]=pi/20, 3pi/20
    A= [tex]\int[/tex](1/2)64cos^2(10[tex]\Theta[/tex]) d[tex]\Theta[/tex]
    Last edited: Oct 18, 2007
  2. jcsd
  3. Oct 18, 2007 #2


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    What you need to do is multiply your answer by 20 since you found the area of one of the 20 petals of the rose curve.
  4. Oct 18, 2007 #3
    Are you having trouble finding the correct solution since yours is too small? or because you don't know how to evaluate the integral?

    If you need help evaluating the integral, use the fact that

    [tex] \cos^2{nx} = \frac{1+\cos{2nx}}{2}, n\in\mathbb{N} [/tex]
  5. Oct 18, 2007 #4
    Okay, let me state what i did in more detail:
    A=(1/2)integral 64(cos^2(10theta)) d(theta)
    =32 integral (1/2)(1+cos20theta) (theta)
    did i do it correct so far?
    then i just plug in my bounds which are pi/20 to 3pi/20 right?
    now should i just multiply my answer by 20?
  6. Oct 18, 2007 #5
    thanks for the help i solved it
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