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Math Help - Parameterisation

  1. #1
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    Parameterisation

    Parameterise:

    1. A cylinder of radius 4, with axis coinciding with the y-axis, starting at y=2 and ending at y=-2. Use trigonometric parameters to parameterise.

    2. The part of a cone x=[(y^2)+(z^2)]^(0.5) , starting at x=0 ending at x=4 with z=>0.

    Help!
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  2. #2
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    Quote Originally Posted by maibs89 View Post
    Parameterise:

    1. A cylinder of radius 4, with axis coinciding with the y-axis, starting at y=2 and ending at y=-2. Use trigonometric parameters to parameterise.

    ...
    Use

    \begin{array}{l}x=4\sin(t) \\ y=s \\z=4\cos(t)\end{array}~,~s \in[-2,2]~\wedge~ t\in[0,2\pi]
    Attached Thumbnails Attached Thumbnails Parameterisation-waagerechtzylinder.gif  
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  3. #3
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    Quote Originally Posted by maibs89 View Post
    Parameterise:



    2. The part of a cone x=[(y^2)+(z^2)]^(0.5) , starting at x=0 ending at x=4 with z=>0.

    Help!
    Use

    \begin{array}{l}x=s\\y=s \cdot \sin(t) \\ z=s\cdot \cos(t)\end{array} ~,~ s \in[0,4]~\wedge~t \in \left[-\frac{\pi}2~,~\frac{\pi}2 \right]

    Remark: You are looking from below into the section of the cone.
    Attached Thumbnails Attached Thumbnails Parameterisation-kegelvonunten.gif  
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  4. #4
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    Are you sure that the second picture is correct? I thought that the x-axis is the symmetry of the cone, i.e the cone should be over the x-axis.
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  5. #5
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    Quote Originally Posted by maibs89 View Post
    Are you sure that the second picture is correct? I thought that the x-axis is the symmetry of the cone, i.e the cone should be over the x-axis.
    The picture is OK. The program places the axes names at the edges of the cube.

    The edge which labeled x runs from 0 to 4.

    The edge which is labeled y runs from -6 to 6. That means the x-axis itself passes exactly through the midpoint of the y-edge.
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  6. #6
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    Quote Originally Posted by maibs89 View Post
    Are you sure that the second picture is correct? I thought that the x-axis is the symmetry of the cone, i.e the cone should be over the x-axis.
    I've attached the graph of the cone again but this time I've removed the orientation cube, I changed the point of view and I've emphasized the positive part of the axes.
    Attached Thumbnails Attached Thumbnails Parameterisation-kegelvonoben.gif  
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