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I am trying to graph a parametric equation on $\mathbb{R}^2$, but Maple keeps giving me an $\mathbb{R}^3$ curve.

Here is what I did

L2 := spacecurve([cos(t), cos(3*t), 0], t = -1 .. 0, axes = framed) display(L2) 

Now I was also stupid enough to use "planecurve" and Maple doesn't recognize it...

2 Answers 2

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Compare the 3d spacecurve,

plots:-spacecurve([cos(t),cos(3*t),0],t=-1..0,axes=box,               labels=[x,y,``],orientation=[-90,0,0]); 

enter image description here

with the 2d curve,

plot([cos(t),cos(3*t),t=-1..0],axes=box); 

enter image description here

That calling sequence of the plot command is called parametric. See the help-page ?plots,parametric or online.

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If you don't specifically need Maple, you can plot it using WolframAlpha.