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**Unformatted text preview: **s worth mentioning that we could have plotted the angles in Example 10.1.3 by ﬁrst converting
them to degree measure and following the procedure set forth in Example 10.1.2. While converting
back and forth from degrees and radians is certainly a good skill to have, it is best that you
learn to ‘think in radians’ as well as you can ‘think in degrees.’ The authors would, however, be
derelict in our duties if we ignored the basic conversion between these systems altogether. Since
one revolution counter-clockwise measures 360◦ and the same angle measures 2π radians, we can
radians
use the proportion 2π 360◦ , or its reduced equivalent, π radians , as the conversion factor between
180◦
the two systems. For example, to convert 60◦ to radians we ﬁnd 60◦ π radians = π radians, or
180◦
3
◦
π
simply 3 . To convert from radian measure back to degrees, we multiply by the ratio π 180 . For
radian
◦
π
180
π
example, − 56 radians is equal to − 56 radians π radians = −15...

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