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92
Chapter 4
•
Radian Measure
§4.2
Example 4.5
A central angle in a circle of radius 5 m cuts off an arc of length 2 m. What is the measure of the
angle in radians? What is the measure in degrees?
Solution:
Letting
r
=
5 and
s
=
2 in formula (4.4), we get:
θ
=
s
r
=
2
5
=
0.4 rad
In degrees, the angle is:
θ
=
0.4 rad
=
180
π
·
0.4
=
22.92
◦
For central angles
θ
>
2
π
rad, i.e.
θ
>
360
◦
, it may not be clear what is meant by the inter
cepted arc, since the angle is larger than one revolution and hence “wraps around” the circle
more than once. We will take the approach that such an arc consists of the full circumference
plus any additional arc length determined by the angle. In other words, formula (4.4) is still
valid for angles
θ
>
2
π
rad.
What about negative angles? In this case using
s
=
r
θ
would mean that the arc length is
negative, which violates the usual concept of length. So we will adopt the convention of only
using nonnegative central angles when discussing arc length.
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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

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