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How to graph polar equations

  1. Feb 29, 2008 #1
    It's my first time here so I guess I have to introduce myself first.

    I am a junior in high school taking Calculus BC and Physics B (taking Physics C next year).
    Currently, as of September 29, 2008, my class is learning of Polar equations.

    We just went over basics but I am not perfectly grasping the concept on using polars.

    One of the question I received during class was:

    r=1/2 + sin([tex]\theta[/tex]

    Now, without using calculator, how do I find the area of the equation which excludes the overlaping part.

    I know that

    A=1/2[tex]\int[/tex]r^2 d[tex]\theta[/tex]
    but here we would subtract the inner area.
    No point in using calculator;;; I cannot check my answer either since my teacher said the right answer choice is not shown (it is a multiple choice question).

    ps. I don't know how to use the "tex" thing so....
    Last edited: Feb 29, 2008
  2. jcsd
  3. Feb 29, 2008 #2


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    Science Advisor

    Well, what have you done? You have given the formula. What do you get when you do the integration? One thing you can do is a quick graph of the region to see what "overlapping" part they are talking about. It's not that difficult even without a calculator! But I'll give you a hint: for [itex]\theta[/itex]= 0 to [itex]\pi[/itex], the graph looks about like an ellipse. For [itex]\theta= \pi[/itex] to [itex]2\pi[/itex], it is a smaller ellipse inside the first one.
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