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Parametric Representation of a Helix

  1. Oct 22, 2007 #1
    Just wanted to check and see if this is right. The k-component of the vector is what I'm unsure of...I've always sucked at converting to parametric form. :)

    1. The problem statement, all variables and given/known data

    Convert to parametric form:
    [tex]x^{2}[/tex] + [tex]y^{2}[/tex] = 9, z = 4arctan(y/x)

    3. The attempt at a solution

    The i- and j-components of the vector are obviously 3cos(t) and 3sin(t), respectively. I'm not sure how the k-component is supposed to turn out...

    Here's my attempt:

    x = 3cos(t)
    y = 3sin(t)
    So, z = 4 arctan [tex]\frac{3sin(t)}{3cos(t)}[/tex] = 4 arctan(tan(t)) = 4t

    Thus, r(t) = [3cos(t), 3sin(t), 4t]
  2. jcsd
  3. Jan 14, 2008 #2
    Looks good to me.
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