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.

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)