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Math Help - polar coordinates question

  1. #1
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    polar coordinates question

    (a) Sketch the curve with polar equation r = a cos 3θ , a > 0, for 0 ≤ θ ≤ pi.
    (b) Show that the total area enclosed by the curve r = a cos 3θ is (pi.a^2)
    /4

    I am able to draw the curve although the answer drew it all the way from 0 to 2pi which I thought didn't make sense given the limits are 0<theta<n - for part b it also finds the area of all 3 of the leafs rather than half which I thought made sense given the limits,

    Thanks,

    Bryn
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  2. #2
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    That's the domain of theta. The function is a function of 3 theta.
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  3. #3
    Moo
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    Hi,

    This is the same problem as here : http://www.mathhelpforum.com/math-he...lar-curve.html

    Though I didn't answer to the main problem yet, because I only have an informal idea of it...

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  4. #4
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    Thanks, could you elaborate on what you mean by it being the domain, I'm not understanding its relevance in this polar coordinates.

    thanks again
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  5. #5
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    Firstly remember for polar coordinates that the r value can be negative, a negative value of r just means it is going 'backwards' so you should appreciate that for example (-r , \pi /2) is the same as (r , 3 \pi /2). To get a rought idea of how r is varying with theta I suggest that you draw the curve y = \cos 3x form 0 to \pi.

    Follow the above carefully and you should be able produce a diagram similar to what moo posted on the other thread. then try and understand why the area is 6 \times 1/2 \int_{0}^{\frac{\pi}{6}}  r^2 d \theta

    Bobak
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