This problem is solved by using the Central Angle Formula, arclength = radius times the central angle. I will show you how to solve a problem where the radius is 15 cm and the central angle is 32 degrees. The angle must be in units of radians to use the formula. To convert 32 degrees to radians, multiply by Pi radians and divide by 180 degrees. This conversion factor cancels the degree units and creates an angle of (32 *3.14156 / 180) radians, or 0.5585 radians. Using the Central Angle Formula, the arc length is 15 cm times 0.5585 radians, or 8.38 cm. The radian units are dropped. This is the answer for the numbers stated in my problem, not your problem. You should be able to follow the pattern of the solution and solve your problem.
This answer is reasonable because 32 degrees is less than 57.3 degrees (the degree equivalent of one radian). If the central angle is one radian the arc length is equal to the radius. If the central angle would have been one radian the arc length would have been 15 cm for my problem.
The answer of 8.38 cm for my problem assumes that "one swing" means motion from the left side to the right side, not "back-and-forth," not a complete cycle, not a complete "tick-tock."
