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Homework Help: Parametric equation

  1. Sep 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that the curve with parametric equation :

    x = sint t;
    y = cos t;
    z = sni^2 t

    is the curve of intersection of the surface z = x^2 and x^2 + y^2 = 1.

    3. The attempt at a solution

    From polor equation I know that x = rcos(t) and y = rsin(t);

    from this we can replace x^2 + y^2 = 1. with cos(t) + sin(t) = 1

    and since z = x^2, and x = rcos(t), it follows that z = r^2cos^2(t) = cos^2(t)

    so we have the vector equation :

    v = < cos(t) , sin(t), cos^2(t).

    But this doesn't follow the question. Whats wrong?
  2. jcsd
  3. Sep 25, 2009 #2


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    The 't' in the polar equations is the theta coordinate in polar coordinates. Your parameter t in the parametric equations is NOT theta. Just show the two x,y,z equations are satisfied for any t.
  4. Sep 25, 2009 #3
    so could I just use, tan(theta) = y/x = sin t / cos t;
    theta = tan ^-1(y/x)
    = tan ^-1 sin t / cos t
    = 1 / tan = cot?
  5. Sep 25, 2009 #4


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    You don't need theta at all. Forget theta. Just work with the original t. This is a question about x,y,z coordinates, not r,theta,z. There is no point in trying to change coordinates. Reread my post 2. Starting with the word "Just".
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