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 θ = 41 ◦ ? Solution: Using formula (4.4) blindly with θ = 41 ◦ , we would get s = r θ = (10)(41) = 410 ft. But this impossible, since a circle of radius 10 ft has a circumference of only 2 π (10) ≈ 62.83 ft! Our error was in using the angle θ measured in degrees , not radians . So ±rst convert θ = 41 ◦ to radians, then use s = r θ : θ = 41 ◦ = π 180 · 41 = 0.716 rad ⇒ s = r θ = (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 θ . This is another reason why radians are so widely used....
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This note was uploaded on 01/21/2012 for the course MAC 1130 taught by Professor Dr.cheun during the Fall '11 term at FSU.
 Fall '11
 Dr.Cheun
 Calculus, Arc Length

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