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I am trying to plot a parametric curve thanks to the the render extension. The curve is called a "trochoid". The thing I don't understand is why the curve is not "perfect", did I do something wrong in the parameters ?enter image description here

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Inkscape's Paramentric Curves extension converts paramentric curves into Bézier curves, which are basically an estimation of the curve. If you don't have enough samples, the curves will be generated with fewer nodes, and will therefore be less accurate and a bit more wonky. Increase the samples to something like 80, and you should see an improvement.

enter image description here

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I would like to add a differing opinion. You can in fact sample with less points and have an ok and perfectly repeatable result. The trick is though that you must sample with a multiple of a period of your function! Offcourse this would require you to do some function analysis.

See your domain is from 0 to 10 with 30 samples. But you should probably sample from 0 to 3 * pi. This way your samples hit the same spot on every sample. Also having 5 samples per period seems like a nonoptimal solution, 4 or 6 would be better

Offcourse the sampling function could be a bit less naive than just number of samples but would be harder to control.

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