To find the length of the arc created by a 60-degree central angle in a circle with a 2-inch diameter, we first determine the radius of the circle. The radius \( r \) is half the diameter, so \( r = 1 \) inch. Next, we convert the 60 degrees into radians since the formula for arc length \( s \) is given in terms of radians. Since \( 360 \) degrees equals \( 2\pi \) radians, \( 60 \) degrees is equal to \( \frac{60}{360} \times 2\pi = \frac{\pi}{3} \) radians. Finally, using the arc length formula \( s = \theta r \), we have \( s = \frac{\pi}{3} \times 1 = \frac{\pi}{3} \) inches. Therefore, the length of the arc is approximately \( 1.05 \) inches when using \( \pi \approx 3.14 \).
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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