This preview shows page 1. Sign up to view the full content.
Unformatted text preview: In a circle of radius r = 10 ft, what is the length s of the arc intercepted by a central angle of measure = 41 ? Solution: Using formula (4.4) blindly with = 41 , we would get s = r = (10)(41) = 410 ft. But this impossible, since a circle of radius 10 ft has a circumference of only 2 (10) 62.83 ft! Our error was in using the angle measured in degrees , not radians . So rst convert = 41 to radians, then use s = r : = 41 = 180 41 = 0.716 rad s = r = (10)(0.716) = 7.16 ft Note that since the arc length s and radius r are usually given in the same units, radian measure is really unitless, since you can think of the units canceling in the ratio s r , which is just . This is another reason why radians are so widely used....
View Full
Document
 Fall '11
 Dr.Cheun
 Calculus, Arc Length

Click to edit the document details