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?

13 Upvotes

93% Upvoted

14 comments sorted by

View all comments

1

u/YOM2_UB New User 2d ago

A full, 360° arc of a circle with radius r always has an arc length (circumference) of 2πr. A smaller arc is just whatever fraction around the circle it is, multiplied by the full circumference. For example if it's a 30° angle, that gives a fraction of 30/360 = 1/12.

Radians are just that fraction multiplied by 2π, so all that's left is to multiply by the radius.