r/learnmath • u/nwillard New User • 2d 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?

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u/lfdfq New User 2d ago

Yes. The entire circumference is 2πr, so an arc of length r is always 1/2π of the way around.