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.

Answer 1

Let us have a denote the measure of the missing arc length.
Since all circles measures 360°, it is then understood that all circles have an angle of 2π .

arc length = central angle
2π circumference

substitute values:
a = 120°
2π 360°
multiply them by 2π and cancel out 2π so you will have
a = 24 π
36
Simplify 24/36 π--2/3π. Thus, the answer to this item is the third option.

(See attached file for clearer work)