Unformatted text preview: Example 10.1.1, successively halving the angle measure until we ﬁnd 58 ≈ 1.96
which tells us our arc extends just a bit beyond the quarter mark into Quadrant III.
4. Since 117 is positive, the arc corresponding to t = 117 begins at (1, 0) and proceeds counterclockwise. As 117 is much greater than 2π , we wrap around the Unit Circle several times
before ﬁnally reaching our endpoint. We approximate 117 as 18.62 which tells us we complete
2π
18 revolutions counterclockwise with 0.62, or just shy of 5 of a revolution to spare. In other
8
words, the terminal side of the angle which measures 117 radians in standard position is just
short of being midway through Quadrant III.
y y 1 1 1 x 1 t = −2 10.1.1 x t = 117 Applications of Radian Measure: Circular Motion Now that we have paired angles with real numbers via radian measure, a whole world of applications
await us. Our ﬁrst excursion into this realm comes by way of circular motion. Suppose an object
is moving as pictured below along a circular path of radius r from the poin...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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