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Math Help - Another Calc III Problem

  1. #1
    Junior Member
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    Angry Another Calc III Problem

    Here's the problem:
    Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point:

    x = e^-t * cos(t)
    y = e^-t * sin(t)
    z = e^-t
    At the point: (1,0,1)

    (It's supposed to be e to the negative t, I just can't get the math software to work properly).

    I know the answer is supposed to be:
    x = 1-t
    y = t
    z = 1-t

    but I have no idea how to get there! Help!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    New York, USA
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    Quote Originally Posted by saxyliz View Post
    Here's the problem:
    Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point:

    x = e^-t * cos(t)
    y = e^-t * sin(t)
    z = e^-t
    At the point: (1,0,1)

    (It's supposed to be e to the negative t, I just can't get the math software to work properly).

    I know the answer is supposed to be:
    x = 1-t
    y = t
    z = 1-t

    but I have no idea how to get there! Help!
    let our curve be given by r(t) = \left< x(t), y(t), z(t) \right> = \left<e^{-t} \cos t, e^{-t} \sin t , e^{-t} \right>.

    note that the line we want is the line passing through the point (1,0,1) with direction vector given by r'(t).

    now we are concerned with when t = 0 (since in that case, x = 1, y = 0 and z = 1, hence we are passing through the point (1,0,1))

    So, you want the line passing through (1,0,1) that has direction vector r'(0)

    i trust you can take it from here
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  3. #3
    Junior Member
    Joined
    Sep 2008
    Posts
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    Thanks! I understand it now!
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