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Homework Help: Parametric equations and polar coordinates

  1. Apr 19, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the area enclosed by the inner loop of the curve r=1-3sinθ

    2. Relevant equations
    A=o.5[itex]\int r^2[/itex] dθ

    3. The attempt at a solution
    I found the integral but i dont know how to find the interval at which i will be integrating from. I tried finding when r=0 and it turns out to be sin^-1(1/3) but it's not a special angle so it would be messy if i plugged that interval in cos(θ).Any hints will be appreciated
  2. jcsd
  3. Apr 19, 2012 #2
    [itex]\sin \theta = \frac{1}{3}[/itex]
    [itex]\cos^2 \theta = 1 - \sin^2 \theta = \frac {8}{9}[/itex]
    [itex]\cos \theta = \pm \frac {2 \sqrt 2}{3}[/itex]
    So it's not a problem. You have to figure out whether it's + or -, depending on theta.
  4. Apr 19, 2012 #3
    the answer had a sin(1/3)^-1 so i think you have to use that as one of your intervals im assuming
  5. Apr 19, 2012 #4


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  6. Apr 19, 2012 #5


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    Do you mean [itex](sin(1/3))^{-1}= 1/sin(1/3))[/itex] or [itex]sin^{-1}(1/3)= arcsin(1/3)[/itex]?
    Last edited by a moderator: Apr 19, 2012
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