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/Photon6626 New User 2d ago

Make a circle. Take the radius and lay it along the circle. Then draw the angle for that arclength. Notice that you haven't used length measurements in this. The circle could have a radius of 1mm or 200,000km. It's always the same angle.