parametrization

[Sneaksuit]

If S is part of the plane z = y - 2 that lies inside the elliptic cylinder x^2 + 4y^2 = 4 and I want to parametrize S I will let
x = 2sin(t)
y = cos(t)
z = cos(t) - 2
I assume this is right but let me know if not. My question is are there any other ways of parametizing S?

[whozum]

I think you ahve your cosins and sins switched. Which direction does your parameter go? Im assuming counter clockwise.

Come to think of it keeping them that way will also work, provided that you aren't going for a specific parametric starting and ending point.

[Sneaksuit]

There is no specific starting point. Do you know of another way parametrizing S though?

[SpaceTiger]

There is no specific starting point. Do you know of another way parametrizing S though?

Basically as he said, make every cosine a sine and the sine a cosine. I suppose you could also add an arbitrary phase shift to the trig functions as well (the sine-cosine reversal is a special case of that).

[Sneaksuit]

So just switch my sin and cosin and that is another way of parametrizing S?

[kleinwolf]

I don't really understand your solution, since apparently you're parametrizing a surface (so you need 2 parameters). I suppose the solution is simply :

x=Rcos(t)\quad y=\frac{R}{2}sin(t)\quad z=\frac{R}{2}sin(t)-2\quad R\in[0;2]\quad t\in[0;2\pi]

[whozum]

So just switch my sin and cosin and that is another way of parametrizing S?

Yes. It will draw the same curve but from a different starting point and direction.

[whozum]

Those parameters would draw the curve of intersection. Parametrizing the entire surface, you would use klein's equation