To find the arc length created by a 60-degree central angle in a circle with a 2-inch diameter, we can first convert the angle from degrees to radians. Since \(360\) degrees is equal to \(2\pi\) radians, we can find that \(60\) degrees is equivalent to \(\frac{60}{360} \times 2\pi = \frac{\pi}{3}\) radians.
Next, we calculate the radius \(r\) of the circle, which is half of the diameter: \(r = \frac{2}{2} = 1\) inch. Using the formula for arc length \(s = r \cdot \theta\), we substitute \(r = 1\) inch and \(\theta = \frac{\pi}{3}\) radians to get the arc length:
\[ s = 1 \cdot \frac{\pi}{3} = \frac{\pi}{3} \text{ inches}. \]
Therefore, the length of the arc is \(\frac{\pi}{3}\) inches.
3 answers