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Unformatted text preview: 1, as in ±igure 4.2.1(a). Clearly, the combined central angle of the two angles has radian measure 1 + 1 = 2, and the combined arc length is r + r = 2 r . r r 1 1 2 r (a) 2 radians r /2 r /2 1/2 1 r (b) 1 2 radian Figure 4.2.1 Radian measure and arc length Now suppose that we cut the angle with radian measure 1 in half, as in ±igure 4.2.1(b). Clearly, this cuts the arc length r in half as well. Thus, we see that Angle = 1 radian ⇒ arc length = r , Angle = 2 radians ⇒ arc length = 2 r , Angle = 1 2 radian ⇒ arc length = 1 2 r , and in general, for any θ ≥ 0, Angle = θ radians ⇒ arc length = θ r , so that θ = arc length radius ....
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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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