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Unformatted text preview: 0◦ .15 Of particular interest is the
fact that an angle which measures 1 in radian measure is equal to 180 ≈ 57.2958◦ . We summarize
these conversions below.
Equation 10.1. Degree - Radian Conversion:
• To convert degree measure to radian measure, multiply by π radians
180◦ • To convert radian measure to degree measure, multiply by 180◦
π radians In light of Example 10.1.3 and Equation 10.1, the reader may well wonder what the allure of radian
measure is. The numbers involved are, admittedly, much more complicated than degree measure.
The answer lies in how easily angles in radian measure can be identiﬁed with real numbers. Consider
the Unit Circle, x2 + y 2 = 1, as drawn below, the angle θ in standard position and the corresponding
arc measuring s units in length. By deﬁnition, the radian measure of θ is r = 1 = s so that, once
again blurring the distinction between an angle and its measure, we have θ = s. In order to
identify real numbers with oriented angles, we make good use of this fact by essentially ‘wrapping’
the real number...
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