In the case of arcs intercepted by a 60 degree central angle, is arc lengths proportional to radius r? If so, what is the constant of proportionality

Question

When the ratio of the values of one variable y to the corresponding values of another variable x is a constant k, y is said to be proportional to x, and the constant k is called the constant of proportionality. Because y/x equals k, you can solved for y to get y=kx

 

what equation gives s in terms of r?

Answer 1

I assume you use the notation s = arc length, r = radius of the circle, and θ, the angle in question.

s=rθ.  Note well that θ is the angle size in radians.

For the particular case of a 60° angle we have

60°=π/3 radians and so the arc length intercepted on a circle of radius r is s=πr/3