Plotting parametric equations in Maple

Question

I have the following problem. Let $\alpha:=\alpha(v)$ and $\beta:=\beta(v)$, where $v\in\mathbb{R}$. Using MAPLE, I would like to plot $\alpha$ and $\beta$ in the $(\alpha,\beta)$ space as $v$ varies continuously. I suspect that this will involve creating lists in Maple. I need some help! Here is what I am thinking at this time:

restart:

alpha:=v-> some function of v:
beta:=v-> some function of v:

for v from 0.01 to 10 by 0.001 do
  alpha:=alpha(v):
  beta:=beta(v):
  ? put the alpha and beta into a list?
od:

?plot the sequence of points in the list?

I need some direction/help from Maple users out there, please.

Answer 1

plot([alpha(v),beta(v),v=0..10]);

No manual lists required.

Answer 2

You can plot a list of points (where each 2D point is represented as a list),

restart:
alpha:=v->sin(v):
beta:=v->cos(v):

plot([seq([alpha(v),beta(v)], v=0.01..10.0, 0.001)]);

Or you could make a parametric plot, optionally forcing the number of points if you wish,

restart:
alpha:=v->sin(v):
beta:=v->cos(v):

plot([alpha(t),beta(t),t=0.01..10.0]);

plot([alpha(t),beta(t),t=0.01..10.0],adaptive=false,numpoints=9991);

See also the plot,parametric help-page.