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Arc Length Question

  1. Oct 7, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the arc length of r(t) = cos(t)^3 i + sin(t)^3 j
    from t = 0 to t = 2 * Pi

    It's a hypocycloid that's four cusped.

    2. Relevant equations
    [tex]s = \int\sqrt{x'^2 + y'^2}[/tex]

    3. The attempt at a solution
    x = cos(t)^3
    y = sin(t)^3

    x' = -3cos(t)^2*sin(t)
    y' = 3sin(t)^2*cos(t)

    [tex]\sqrt{x'^2 + y'^2}[/tex] = 3* [tex]\sqrt{cos(t)^4*sin(t)^2 + sin(t)^4*cos(t)^2}[/tex]

    That simplifies to [tex]s = \int 3*\sqrt{1}[/tex]

    So the answer is 6*Pi, but for some reason Maple throws out 6.
  2. jcsd
  3. Oct 7, 2008 #2


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    Science Advisor
    Homework Helper

    The radical doesn't simplify to 1. Check that again.
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