To find the arc length created by a 60-degree central angle in a circle with a 2-inch diameter, we first need to convert the angle from degrees to radians. Since 360 degrees is equivalent to \(2\pi\) radians, 60 degrees is \(\frac{60}{360} \times 2\pi = \frac{\pi}{3}\) radians.
Next, we can use the formula for arc length, \(s = \theta \cdot r\), where \(r\) is the radius. The radius \(r\) of our circle is half of the diameter, so \(r = 1\) inch. Therefore, substituting in the values, we have:
\[ s = \left(\frac{\pi}{3}\right) \cdot 1 = \frac{\pi}{3} \text{ inches}. \]
Thus, the length of the arc created by a 60-degree angle in this circle is \(\frac{\pi}{3}\) inches.
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