Unformatted text preview: that a positive
measure indicates counterclockwise rotation and a negative measure indicates clockwise rotation.14
Two positive angles α and β are supplementary if α + β = π and complementary if α + β = π .
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Finally, we leave it to the reader to show that when using radian measure, two angles α and β are
coterminal if and only if β = α + 2πk for some integer k .
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14 The authors are well aware that we are now identifying radians with real numbers. We will justify this shortly.
This, in turn, endows the subtended arcs with an orientation as well. We address this in short order. 602 Foundations of Trigonometry Example 10.1.3. Graph each of the (oriented) angles below in standard position and classify them
according to where their terminal side lies. Find three coterminal angles, at least one of which is
positive and one of which is negative. 1. α = π
6 π
2. β = − 43 3. γ = 9π
4 π
4. φ = − 52 Solution.
1. The angle α = π is positive, so we draw an angle with its initial side on the positive xaxis and
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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