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Find Area with Theorem of Green - center - radius

  1. Nov 25, 2015 #1
    1. The problem statement, all variables and given/known data
    x(t) = 6cos(t)−cos(6t) y(t) = 6sin(t)−sin(6t) 0 <= t <= 2*pi
    I need to find the area cm2 with Th Green.

    I need to find the radius and the center coordinate

    2. Relevant equations


    3. The attempt at a solution
    $ = integral
    1/2* ( 2*pi$0 ((x)dy - (y)dx) dt )

    1/2 (2*pi$0 ((6cos(t)−cos(6t)*6cos(t)−6cos(6t) - (6sin(t)−sin(6t)*6sin(t)−6*sin(6t)) dt)

    = 42*pi

    How do I find the center? is it (0,0)?
     
  2. jcsd
  3. Nov 25, 2015 #2

    RUber

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    Homework Helper

    The center should be (0,0). This can be shown rather clearly by saying that
    ##x_1(t)=6 \cos (t)\quad y_1(t) =6\sin(t)## is a circle centered at (0,0),
    and so is ##x_2(t)=\cos (6t)\quad y_2(t) =\sin(6t)##.

    I am finding it difficult to read your work. Please work with Tex if you can.
    If I can read it, it should say:
    ## \text{Area} = \frac12 \int_0^{2\pi} \left( 6 \cos (t)-\cos (6t) \right) \left( 6 \cos (t)-6\cos (6t) \right) - \left( 6\sin(t)-\sin(6t) \right) \left( - 6\sin(t) + 6\sin(6t) \right) \, dt ##
    Which gives 42pi.
     
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