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Unformatted text preview: radian measure t.
y y 1 y 1 1 s
x 1 On the Unit Circle, θ = s. t
1 x Identifying t > 0 with an angle. t x 1 t Identifying t < 0 with an angle. Example 10.1.4. Sketch the oriented arc on the Unit Circle corresponding to each of the following
1. t = 3π
4 2. t = −2π 3. t = −2 4. t = 117 Solution.
1. The arc associated with t = 34 is the arc on the Unit Circle which subtends the angle 34 in
radian measure. Since 4 is 8 of a revolution, we have an arc which begins at the point (1, 0)
proceeds counter-clockwise up to midway through Quadrant II. 2. Since one revolution is 2π radians, and t = −2π is negative, we graph the arc which begins
at (1, 0) and proceeds clockwise for one full revolution.
y y 1 1 1 t= 3π
4 x 1 t = −2π x 10.1 Angles and their Measure 605 3. Like t = −2π , t = −2 is negative, so we begin our arc at (1, 0) and proceed clockwise around
the unit circle. Since π ≈ 3.14 and π ≈ 1.57, we ﬁnd that rotating 2 radians clockwise from
the point (1, 0) lands us in Quadrant III. To more accurately place the endpoint, we proceed
as we did in...
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