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

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.

• Are you saying that a third of $2\pi$ is $\frac13\pi$? – Arthur Apr 30 at 9:22
• The answer is 3). The circumference of the unit circle is $2 \pi$ and you are taking it as $\pi$. – Kavi Rama Murthy Apr 30 at 9:22
Angle ,$$\theta$$(in radians) = arc-length/ radius = $$\frac{s}{r}$$
We have $$r=1$$ and $$\theta = 120^o = 2\pi/3$$
So, $$s=r\theta = 1.2\pi/3 = 2\pi/3$$