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Homework Help: Representing a curve with a vector valued function

  1. Sep 21, 2010 #1
    1. The problem statement, all variables and given/known data
    See attached image


    2. Relevant equations



    3. The attempt at a solution

    Why use x=2sint??

    Would it be incorrect to use the x=2cost (versus the given x=2sint)? My professor instructed us to not use the given parameters in the book and to come up with our own, and I would of used x=2cost which would of changed the resulting vector-valued function (Resulting in r = 2Cos(t)i+2Sin(t)j+4Cos2tk)

    Thanks.
     

    Attached Files:

  2. jcsd
  3. Sep 21, 2010 #2

    Dick

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    Either one is fine. The difference between the two is also the same thing as changing the parameter t into pi/2-t. Do you see why?
     
    Last edited: Sep 21, 2010
  4. Sep 21, 2010 #3
    I understand the identity sin(t)=cos[(pi/2)-t], but I really don't see why using either parameters x=2sint or x=2cost is equivalent. The book wants me to use x=2sint, wouldn't the equivalent then be actually x=2cos([(pi/2)-t]) ? Thanks
     
  5. Sep 21, 2010 #4

    Dick

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    If r(t) is a curve then r(a-t) represents the same curve. It goes through the same points, just at different values of t.
     
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