[Math] the length of the arc on the unit circle subtended by an angle of 120 degrees? Show all work.

Question

What is the length of the arc on the unit circle subtended by an angle of 120 degrees? Show all work.

1. 2/3
2. 1/3(pi)
3. 2/3(pi)
4. pi

I used an equation where the central angle equals the arc length divided by the radius. Since 120 degrees is 1/3 of the total circumference of 360 degrees (or 2pi), I chose the answer to be 2.

Is my answer correct? If not, please explain why.

Answer 1

Angle ,$ \theta$(in radians) = arc-length/ radius = $\frac{s}{r}$

We have $r=1$ and $\theta = 120^o = 2\pi/3$

So, $s=r\theta = 1.2\pi/3 = 2\pi/3$