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Finding area in polar coordinates

  • Thread starter raincheck
  • Start date
  • #1
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Homework Statement


"Find the area of the region described: The region that is enclosed by the rose r=4cos3[theta]"


Homework Equations



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

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:

Answers and Replies

  • #2
370
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I get 8pi as well.
 
  • #3
38
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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 :[
 
  • #4
370
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That's a really weird graph intersection. Where did you get that question from?
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
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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?
 

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