Unit circle wit sin in desmos

[Rebello]

Hello
On Wikipedia you can find this animation:

I want to rebuild it like this:

where you can use X_1 to set the angle.

So I have an angle alpha which can be controlled by the point X_1.

my current state is this:

in the beginning everything is fine.
But:
When alpha gets over \pi/2, alpha doesn’t follow continuously along anymore.

I tried to rebuild the same project, to get new ideas on how to fix that. But now I am not able at all to make alpha work correctly. Not even for angles smaller than pi/2.

I dont want to restrict alpha to be between 0 and 2\pi.

My project

[Mike_Gleeson]

Not entirely sure what you want but does this do? Untitled Graph | Desmos

[Rebello]

thank you so much. I am missing this little angle in the triangle

[Daniel_Grubbs]

Here you go. I edited @Mike_Gleeson’s graph to include the arc.
Two edits needed to display it properly you may not notice:

1. I confined the bounds of a from 0 to 2pi.
2. I changed a in the definition of P to a modular calculation. This allows you to continuously move the point in a circle, rather than stopping at 2pi and having to return back to 0 by rotating back clockwise.

(Edit: I initially had the arc from 0 rather than in the triangle. Fixed!)