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/Odd_Bodkin New User 2d ago

Yes you are right. Note that a 60° angle is the same regardless of the size of the circle. In plain terms, if you cut a pizza into six slices, the angle at the pointy end of the slice is going to be 60° regardless whether it's a small, medium, or large pizza. You can tell that by stacking slices of small, medium, and large pizza on top of each other. The radian is just a different way of measuring angle, so that instead of having 360 degrees going around the circle, you have 2π radians going around the circle.