Setting max or min of interval without endpoint included when plotting (Manipulate, Animate)

Question

I imagine this question has been asked before so I apologize if this is a duplicate, but I could not find anything that answers my questions (will happily delete if I can be linked to the appropriate question with an answer).

I am trying to illustrate for my students how parametric curves are plotted, and I thought the following useful:

Animate[ParametricPlot[{Sin[2 x], Cos[6 x]}, {x, 0, n1},PlotRange -> {{-1, 1}, {-1, 1}}], {n1, 0, Pi}]

However, the animation begins by throwing an error: something about endpoints for x in the chosen interval must have distinct machine-precision numerical values. I assume the issue is because I have x ranging from $0$ to n1, where n1 ranges from $0$ to $\pi$. Thus, going from $0$ to $0$ at first is an issue.

Question: Is there a way I can have n1 vary from $0$ to $\pi$ without including $0$? Essentially, is there a way to not include the max or min or both for a chosen interval, where it may be akin to me saying to someone, "Plot the curve as $t$ ranges from $0$ to $\pi$, but make sure you do not include $0$."

The problem (or what I perceive to be the problem) carries over to uses of Manipulate as well such as if I wanted to look at Manipulate[1/i, {i, 0, 10}] where it's clear I do not want to actually start at $i=0$ but as close to it as possible from the right-hand side.

Answer 1

You can manually set the starting value for your variable to a very small, non-zero value. You could use e.g. $MinMachineNumber instead of $0$ in your lower bound for n1 in Animate. It seems to work fine:

Animate[
 ParametricPlot[{Sin[2 x], Cos[6 x]}, {x, 0, n1}, PlotRange -> {{-1, 1}, {-1, 1}}],
 {n1, $MinMachineNumber, Pi}
]