To determine the arc length created by a 60-degree central angle in a circle with a 2-inch diameter, we first need to calculate the radius. The radius \( r \) is half of the diameter, so \( r = \frac{2}{2} = 1 \) inch. Since 60 degrees is equivalent to \( \frac{1}{6} \) of a full circle (360 degrees), we can use the formula for arc length \( s = r\theta \) where \( \theta \) is in radians. Converting 60 degrees to radians gives us \( \theta = \frac{60 \times \pi}{180} = \frac{\pi}{3} \) radians. Thus, the arc length \( s = 1 \times \frac{\pi}{3} = \frac{\pi}{3} \) inches.
The formula for the circumference of a circle is C=πd, where C= circumference and d= diameter. It can also be defined as C=2πr, where r= radius. If 360 degrees =2π radians, and the formula for arc length is θ=sr, then determine the length created by a 60-degree central angle in a circle with a 2-inch diameter and explain how you found it. Answer in 3–5 sentences.(4 points)
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