Ohhh, a triangular sheet ‘spinning’ into a cone shape? Hmmmm. That’d need something funky with curve modifiers and vertex groups, which is a little more advanced. Or… Uh… Yeah. Something crazy like that. XD
Or. On another note. You could make a cone, then split an edge so it wasn’t continuous, then set the view to top-down and set the cursor to the middle of the cone. Then just set the rotation/scaling pivot to ‘cursor’, manually rotate all the edgeloops in the cone into one space so it looks like you just have one triangle, then turn THAT into a shape key so you could slide it back and forth to make sort of a ‘extrude/stretch’ type deal. If you want, you could flatten the resulting ‘fake triangle’ as well.
Of course, this is all off the top of my head, since I’ve never done anything all crazy and geometrical like you’re talking about. So, be warned, that as well as being intensely confusing, it may not work, either. Just a suggestion, though.
EDIT: And clhannah, you’re right, I feel kind of an idiot for not noticing before.