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Unformatted text preview: revolution.3 For instance, the measure of an angle which
represents a rotation of 3 of a revolution would measure 3 (360◦ ) = 240◦ , the measure of an angle
which constitutes only 12 of a revolution measures 12 (360◦ ) = 30◦ and an angle which indicates
no rotation at all is measured as 0◦ . 240◦ 30◦ 0◦ Using our deﬁnition of degree measure, we have that 1◦ represents the measure of an angle which
constitutes 360 of a revolution. Even though it may be hard to draw, it is nonetheless not diﬃcult
to imagine an angle with measure smaller than 1◦ . There are two way subdivide degrees. The
ﬁrst, and most familiar, is decimal degrees. For example, an angle with a measure of 30.5◦ would
represent a rotation halfway between 30◦ and 31◦ , or equivalently, 30.5 = 720 of a full rotation. This
can be taken to the limit using Calculus so that measures like 2 make sense.4 The second way
to divide degrees is the Degree - Minute - Second (DMS) system. In this system, o...
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