Question

Explain how arc length and the measure of the central angle of a circle are related.

Answer 1

This is simple unitary method. A full circle has an angle of \(360^{o} \text{ or } 2\pi \text{ radians}\). This full circle corresponds to an arc length = to the circumference = \(2\pi r\)

Thus, an angle of \(1^{o}\) corresponds to an arc length of \(2\pi r/360\) and an angle of \(1\) radian corresponds to an arc length of \(2\pi r/2\pi = r\).

Now, if the central angle is \(\theta^{o}\), then the corresponding arc length is given by \(\theta\times 2\pi r/360\)
If the central angle is \(\theta\) radians, then the corresponding arc length is given by \(\theta \times r\)

Answer 2

thank you!