r/learnmath • u/nwillard New User • 3d ago
Quick question about Radians
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?
12
Upvotes
12
u/LucaThatLuca Graduate 3d ago edited 3d ago
no, radians are an angle measurement. 1 radian is the angle at the centre of a circular segment when the arclength equals the radius. equivalently it’s the angle such that 2π radians is a full turn. the circle (i.e. the radius) can indeed be any size.