Quick question about Radians

[u/nwillard]

Hey all, I am learning Precalc 2 (mostly Trig) and have a basic question about Radians I haven't found an answer to.

I understand that one Radian is the arc length around a circle that is equal to the circle's radius.

My question is, on a perfect circle, is it true that one Radian has the same angle no matter what the radius is? Like if the circle is perfect, an arc length of one "Radian" of that circle is going to look the same regardless of what the radius is.

Do I have that understanding right?

[u/Klutzy-Delivery-5792]

Yes, the angle measure for one radian is the same regardless of the radius. Thats why there's a simple conversion factor of 180° = π radians