Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Finding area in polar coordinates

  1. Feb 28, 2007 #1
    1. The problem statement, all variables and given/known data
    "Find the area of the region described: The region that is enclosed by the rose r=4cos3[theta]"

    2. Relevant equations

    A= [integral] (1/2)r^2 d[theta]

    3. The attempt at a solution

    I'll use Q as [theta]..

    I'm not really sure, but I set up (1/2) [integral] (16(cos^2)3Q) dQ

    .. then I thought we were supposed to use the identity (cos^2)Q = (1/2)(1+cos2Q), but every time I substitute this in and integrate, I get 8[pi] instead of 4[pi], the correct answer. What am I doing wrong?

    Thank you so much :]
    Last edited: Feb 28, 2007
  2. jcsd
  3. Feb 28, 2007 #2
    I get 8pi as well.
  4. Feb 28, 2007 #3
    hmmm, I asked someone else and they got 8pi too...

    Well I had one more question... if I were finding the area between
    r = sqrt[cos2(theta)] and
    r = 2cos(theta)

    do I basically do the same thing as finding the area between two regular curves? Each time I try it, I come up with zeros and I feel like that cant be right :[
  5. Mar 1, 2007 #4
    That's a really weird graph intersection. Where did you get that question from?
  6. Mar 1, 2007 #5


    User Avatar
    Science Advisor

    You don't say anything about what limits of integration you used. [itex]\theta[/itex] going from 0 to what traces that figure exactly once?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook