How do I draw precise arcs, then make the line thicker at one end, so it kind of looks like an eyebrow?

Artistic Media tool?

You can draw directly with it, but it can also be applied to an existing Curve.

leknugas said:

I've been trying to apply it to an existing curve, but have not figured out how to do it. :-)

When I first tried to do it, I also found it difficult - because there is no "Apply" button on the Property Bar that is displayed for Artistic Media.

With the Artistic Media tool selected, click on the Curve to select it, then try adjusting the Stroke Width in the Property Bar that is displayed for Artistic Media. The change causes Artistic Media to be applied or update.

That's one way to do it. Another way is to use the Artistic Media docker, which makes it easier to see/apply presets, brushes, etc., but doesn't provide access to all of the settings that the Property Bar does.