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Parametric equations graph

  1. Jan 26, 2009 #1
    1. The problem statement, all variables and given/known data
    In the xy-plane, the curve with parametric equations x=cost and y=sint, 0<=t=<pi, has what length?

    3. The attempt at a solution

    I drew the graphs x=cost and y=sint and shaded the area where the graphs intersect between 0 and pi. I don't know where to go from here.
     
  2. jcsd
  3. Jan 26, 2009 #2

    Mark44

    Staff: Mentor

    You should have one graph, with (x, y) coordinates, where both x and y depend on t. That's what parametric equations are about. Try plotting about 10 points and see what you get.
     
  4. Jan 26, 2009 #3

    AEM

    User Avatar
    Gold Member

    The fact that you shaded in an area indicates that you are thinking in terms of area, not length along the curve that was suggested to you. You should have an equation for arc length to work with. Try this one:

    [tex] S = \int_0 ^ \pi \sqrt{ dx^2 + dy^2} dt [/tex]

    Now it's up to you to figure out dx and dy. I think you'll find the answer is very simple.
     
  5. Jan 26, 2009 #4

    Dick

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    Science Advisor
    Homework Helper

    I think you mean sqrt((dx/dt)^2+(dy/dt)^2) for the integrand. But otherwise, good advice.
     
  6. Jan 26, 2009 #5

    Mark44

    Staff: Mentor

    All well and good, but the parametric curve of this problem is simple enough that its length can be obtained without resorting to an integral.
     
  7. Jan 26, 2009 #6

    Dick

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    Science Advisor
    Homework Helper

    Yeah, sure. But the integral is SO EASY. It's not that much easier to remember the formula than to just derive it, if you are doing calculus. It's that easy. Certainly easier than plotting out 10 points.
     
  8. Jan 27, 2009 #7
    Hint: (Zcos t, Zsin t) where Z is a some arbitrary constant(in the set +R) represents a circle. In your case, substitute Z=1, 0<t<pi.
     
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