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Parametric equations

  1. Oct 9, 2006 #1
    Let L be the circle in the x-y plane with center the origin and radius 57.
    Let S be a moveable circle with radius 30 . S is rolled
    along the inside of L without slipping while L remains fixed.
    A point P is marked on S before S is rolled and the path of P is studied.
    The initial position of P is (57,0).
    The initial position of the center of S is (27,0) .
    After S has moved counterclockwise about the origin
    through an angle t the position of P is
    x= 27 \cos t + 30 \cos \left( \frac{9}{10} t \right)
    y= 27 \sin t - 30 \sin \left( \frac{9}{10} t \right)
    How far does P move before it returns to its initial position?
    Hint: You may use the formulas for cos( u+v) and sin( w /2).
    S makes several complete revolutions about the origin before P returns to (57,0).

    I tried taking the derivative of the x and y equations, each squared and added together and took the square root of that sum from 0 to 57. Apparently that was the wrong method, but I was wondering how I could go about doing this problem.
     
  2. jcsd
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