1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    sharks

    User Avatar
    Gold Member

  6. Apr 19, 2012 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    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: Apr 19, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Parametric equations and polar coordinates
Loading...