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Parametric equations

  1. Sep 27, 2005 #1
    need parametric equations to the tangent line at the point
    (cos 0pi/6, sin 0pi/6, 0pi/6) on the curve x = cost, y = sint, z = t

    x(t) = ?

    now from my understanding, i have to find the derivatives of x, y, and z right? and i did this... now alll i should do is plug in the x, y, z pts? and get the answers? i dont know if the 0pi/6 is correct cuz it was printed in w/ the problem... it could be pi/6 only and not 0pi/6.... could someone help maybe i did some kind of calculation error.... if possible explain thanks
  2. jcsd
  3. Sep 27, 2005 #2
    anyone know how to help here???
  4. Sep 28, 2005 #3
    Think of your function as a basic space curve:
    [tex] \vec r\left( t \right) = \left\langle {\cos t,\sin t,t} \right\rangle [/tex]

    [tex] \vec r\,'\left( t \right) = \left\langle { - \sin t,\cos t,1} \right\rangle [/tex]

    Your point, [tex] \left( {1,0,0} \right) [/tex], can be represented by the positional vector [tex] \vec r \left( 0 \right) [/tex].

    As you remember from earlier calculus, the tangent line will thus be parallel to
    [tex] \vec r \, ' \left( 0 \right) = \left\langle {0,1,1} \right\rangle [/tex]

    Now that you have an equation, you can represent the tangent line as :smile: :
    [tex] \vec L\left( t \right) = \left\langle {1,0,0} \right\rangle + t\left\langle {0,1,1} \right\rangle \Rightarrow \vec L\left( t \right) = \left\langle {1,t,t} \right\rangle [/tex]

    Or parametrically without vector notation:
    [tex] L\left( t \right) = \left\{ \begin{gathered}
    x = 1 \hfill \\
    y = z = t \hfill \\
    \end{gathered} \right\} [/tex]

    :biggrin: Which basically says:
    [tex] x = 1 , \,y = z[/tex]

    **Hope this helps :smile:
    Last edited: Sep 28, 2005
  5. Sep 28, 2005 #4
    so what is x(t)=? y(t)=? z(t)=? cuz i see what u did but the computer say its wrong.... so i dontk now where it went wrong... i know what u did i did the same..
  6. Sep 28, 2005 #5
    [tex] \left\{ \begin{gathered}
    x\left( t \right) = 1 \hfill \\
    y\left( t \right) = t \hfill \\
    z\left( t \right) = t \hfill \\
    \end{gathered} \right\} [/tex]

    What's the problem?
    Last edited: Sep 28, 2005
  7. Sep 28, 2005 #6
    well x(t) is not 1+t and same w/the others.. the computer say its wrong... thats what trippin me out
  8. Sep 28, 2005 #7
    wow now the y(t) and z(t) is right but the x(t) is still wrong...
  9. Sep 28, 2005 #8
    yay its just 1....
  10. Sep 28, 2005 #9
    thanks alot dude!! u helped alot i hate cal 3 its just hard for me for some reasons... its the vectors... i cant picture them...
  11. Sep 28, 2005 #10
    No problem :smile: Welcome to PF
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