Sure, let's find the arc length of an angle [tex]\(\frac{\pi}{3}\)[/tex] radians on a unit circle.
The formula for the arc length [tex]\( s \)[/tex] of a circle is given by:
[tex]\[ s = r \theta \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the circle,
- [tex]\( \theta \)[/tex] is the angle in radians.
In this case, we are dealing with a unit circle, which means the radius [tex]\( r = 1 \)[/tex].
The given angle [tex]\( \theta \)[/tex] is [tex]\(\frac{\pi}{3}\)[/tex] radians.
Now, substituting the values into the formula:
[tex]\[ s = 1 \cdot \frac{\pi}{3} = \frac{\pi}{3} \][/tex]
Thus, the arc length for an angle of [tex]\(\frac{\pi}{3}\)[/tex] radians on a unit circle is:
[tex]\[ \frac{\pi}{3} \][/tex]
This matches with option C:
C [tex]\(\frac{\pi}{3}\)[/tex]
