1. ## 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!

2. Originally Posted by maibs89
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

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

3. Originally Posted by maibs89
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

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

Remark: You are looking from below into the section of the cone.

4. 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.

5. Originally Posted by maibs89
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.

6. Originally Posted by maibs89
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.