Thread: Finding a parametric representation of the surface, (vector calculus) please help me

Consider the surface z=thaita (sorry i dont know how to spell it) in cylindrical coordinates shown in figure 3. Find aparametric representation of this surface

I dont even know where to start, please help me out
thanks

I'll try and help you out, I've never really used cylindrical co-ordinates but I do know that they're defined by three properties; the radial distance from the z-axis, the azimuth (angle to) of the point and height z.
Your equation would result in a straight line on the z-axis since the distance from the z-axis isn't mentioned. Are you sure the equation is correct as it clearly doesn't correspond with the diagram.

Try it, let , and on this grapher, the result is just a straight line.
surf_graph_cylin

Why ?
Try the plotter with , to and to

Hmmm, I understand what you're saying, but if r isn't explicitly defined surely that means it's either irrelevant hence or it's true for all values of r: , why would the equation imply that ?

I'm not criticising you, just brainstorming. =)

I think an appropriate parametric representation would be:







where: and

That does seem a bit silly but it's all I've got at the moment.

I chose (and for no particular reason other than it gives a reasonable plot (and produces something like the surface shown in the original question) whereas does not. Just for example really.
If there are no limits specified then I think is correct, afterall if you were asked to plot, in [2D], for example, you would draw, or at least imply, a line of infinite length, not a single point at

If the diagram weren't present I'd think the answer I gave was correct but I'm thinking that some information is missing. Given how the diagram looks







where: and

...doesn't seem possible.