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)

Question

all in word form

Answer 1

To determine the length of the arc created by a sixty-degree central angle in a circle with a two-inch diameter, I first needed to find the radius. The radius is half of the diameter, so it is one inch. Next, I converted the angle from degrees to radians because the formula for arc length requires radians. Since sixty degrees is equivalent to one-third of two pi radians, I then used the arc length formula, which is the product of the angle in radians and the radius. Therefore, I calculated the arc length by multiplying one-third of two pi (which equals two pi over three) by one inch, resulting in an arc length of two pi over three inches.