How do you find arc length?

Answer 1

We know that there are 2pi radians in a full circle with radius r. We also know that the circumference (arc length) of a circle with radius r is 2pir. So we can say that:

The arc length = measure of central angle in radians x radius length.

Let

s = arc length

θ = measure of central angle in radians, and

r = radius,

then, the arc length formula has the general form: s = θr If θ is in degrees, then s = θ/360 x 2pir
There are multiple ways, depending on the information you are given.

For y = f(x), x in (a, b):

s = integral(a, b, sqrt{1 + [f'(x)]2}dx)

For r(t) = , t in (a, b):

s = integral(a, b, |r'(t)|dt) = integral(a, b, sqrt{[x'(t)2] + [y'(t)]2}dt)

Answer 2

An arc length is part of the circumference of a circle.