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Find parametric equations for the tangent line at the point

  1. Sep 28, 2009 #1
    1. The problem statement, all variables and given/known data
    Find parametric equations for the tangent line at the point

    [tex](\cos(\frac{4 \pi}{6}) ,\sin(\frac{4 \pi}{6}) ,\frac{4 \pi}{6}) )[/tex]

    on the curve


    [tex]x=\cos t,\ y=\sin t, \ z=t [/tex]

    2. Relevant equations



    3. The attempt at a solution
    Took the derivative
    r'(t)=( -sint, cost, 1)

    Here's where I start to fall apart...I'm not sure what to do...but..is this close...

    cos(4pi/6)= -1/2

    r'(-1/2) = (-sin(-1/2), cos(-1/2), 1)

    so,

    x= (-1/2) + (-sin(-1/2))t
    y= (sin(4pi/6)) + (cos(-1/2)t
    z= 4pi/6 + t

    So where did I go wrong? I hope I'm not that far off. If anything needs clarified, please ask.
     
  2. jcsd
  3. Sep 28, 2009 #2

    lanedance

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    Homework Helper

    based on what you have said why choose the point t = -1/2? i would think t = 4.pi/6 is a better choice ;) and what the question asks for

    then once you have the tangent vector r', and teh point of the curve say p, the equation o teh tangent line will be

    f(s) = s.r'+p
     
  4. Sep 28, 2009 #3
    Thank you! I have the right answer, but I don't understand why you chose t= 4pi/6..can you explain?
     
  5. Sep 28, 2009 #4

    lanedance

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    Homework Helper

    compare you original parametric equations with teh point you are asked to evaluate it at, this gives you the correct t value
     
  6. Sep 28, 2009 #5
    Ohhh. Yikes, I can't believe I didn't notice that! Thanks again!
     
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