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Math Help - Area between two polar equations

  1. #1
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    Area between two polar equations

    Hi,

    I am asked to solve the region R bounded inside of r = 1+cos(4theta) and outside r = 2. Now I know I need to find the points of intersections, by equaling both equations. So I find theta to be pi/32, 3pi/32, etc. First equation is, does it make sense? I mean I have drawn the graph of both:
    Area between two polar equations-20120922_165121.jpg

    Hum sorry, picture is rotated counter-clock wise. 0 is at the top. Anyhow, does it make sense that the first point of intersection hits at pi/32? and second, is it a legit move, to take the integral from o to pi/32, and by symmetry, multiply it by 8 to get the area of all the "petals", since my area I blacked is symmetric to the other side.

    Thanks,

    R.
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  2. #2
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    Re: Area between two polar equations

    Hello, richardsim10!

    Is there a typo? .Or is it a trick question?
    I find no area at all!


    \text{I am asked to find the area inside of }r \:=\: 1+\cos4\theta\,\text{ and outside }\,r \,=\, 2.

    r\,=\,2 is a circle, center at the Origin (pole) with radius 2.

    r \:=\:1+\cos4\theta is a 4-leaf rose curve whose petals are 2 units long.

    That is, it never ventures outside of the circle . . .

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  3. #3
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    Re: Area between two polar equations

    I made a typo indeed. It is r = 2+cos(4theta). So petals are 3 units long. Sorry again, my bad.
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  4. #4
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    Lightbulb Re: Area between two polar equations

    Quote Originally Posted by richardsim10 View Post
    to solve the region R bounded inside of r = 2+cos(4theta) and outside r = 2.
    Attached Thumbnails Attached Thumbnails Area between two polar equations-area-between-2-polar-functions.png  
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  5. #5
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    Re: Area between two polar equations

    I finally managed to find my mistake. Angle is not pi/32, bur rather pi/8. I just made a stupid mental mistake.
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