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
18 revolutions counter-clockwise with 0.62, or just shy of 5 of a revolution to spare. In other
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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