College Trigonometry, 2011a

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696 Foundations of <strong>Trigonometry</strong> 117 ◦ 15 ′ 45 ′′ = 117 ◦ +15 ′ +45 ′′ = 117 ◦ + 1 ◦ 4 + 1 ◦ 80 = 9381 ◦ 80 = 117.2625 ◦ Recall that two acute angles are called complementary angles if their measures add to 90 ◦ . Two angles, either a pair of right angles or one acute angle and one obtuse angle, are called supplementary angles if their measures add to 180 ◦ . In the diagram below, the angles α and β are supplementary angles while the pair γ and θ are complementary angles. β θ α γ Supplementary Angles Complementary Angles In practice, the distinction between the angle itself and its measure is blurred so that the sentence ‘α is an angle measuring 42 ◦ ’ is often abbreviated as ‘α =42 ◦ .’ It is now time for an example. Example 10.1.1. Let α = 111.371 ◦ and β =37 ◦ 28 ′ 17 ′′ . 1. Convert α to the DMS system. Round your answer to the nearest second. 2. Convert β to decimal degrees. Round your answer to the nearest thousandth of a degree. 3. Sketch α and β. 4. Find a supplementary angle for α. 5. Find a complementary angle for β. Solution. 1. To convert ( ) α to the DMS system, we start with 111.371 ◦ = 111 ◦ +0.371 ( ) ◦ . Next we convert 0.371 ◦ 60 ′ 1 =22.26 ′ .Writing22.26 ′ =22 ′ +0.26 ′ , we convert 0.26 ′ 60 ′′ ◦ 1 =15.6 ′′ . Hence, ′ 111.371 ◦ = 111 ◦ +0.371 ◦ = 111 ◦ +22.26 ′ = 111 ◦ +22 ′ +0.26 ′ = 111 ◦ +22 ′ +15.6 ′′ = 111 ◦ 22 ′ 15.6 ′′ Rounding to seconds, we obtain α ≈ 111 ◦ 22 ′ 16 ′′ .
10.1 Angles and their Measure 697 2. To convert β to decimal degrees, we convert 28 ′ ( ) 1 ◦ 60 = 7 ′ it all together, we have 15 37 ◦ 28 ′ 17 ′′ = 37 ◦ +28 ′ +17 ′′ = 37 ◦ + 7 = 134897 3600 ≈ 37.471 ◦ 15 ◦ ◦ and 17 ′′ ( ) 1 ◦ 3600 = 17 ◦ ′ 3600 . Putting ◦ + 17 ◦ 3600 3. To sketch α, wefirstnotethat90 ◦
Page 1 and 2: College Trigonometry Version ⌊π
Page 3 and 4: Table of Contents vii 10 Foundation
Page 5 and 6: Preface Thank you for your interest
Page 7 and 8: xi text and we have gone to great l
Page 9 and 10: Chapter 10 Foundations of Trigonome
Page 11: 10.1 Angles and their Measure 695 k
Page 15 and 16: 10.1 Angles and their Measure 699 4
Page 17 and 18: 10.1 Angles and their Measure 701 T
Page 19 and 20: 10.1 Angles and their Measure 703 y
Page 21 and 22: 10.1 Angles and their Measure 705 y
Page 23 and 24: 10.1 Angles and their Measure 707 h
Page 27 and 28: 10.1 Angles and their Measure 711 I
Page 33 and 34: 10.2 The Unit Circle: Cosine and Si
Page 53 and 54: 30 ◦ 1 10.2 The Unit Circle: Cosi
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10.3 The Six Circular Functions and
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10.4 Trigonometric Identities 771 f
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10.4 Trigonometric Identities 773 2
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10.4 Trigonometric Identities 779 T
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10.4 Trigonometric Identities 781 R
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10.4 Trigonometric Identities 785 I
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10.5 Graphs of the Trigonometric Fu
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10.6 The Inverse Trigonometric Func
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10.7 Trigonometric Equations and In
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Chapter 11 Applications of Trigonom
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11.1 Applications of Sinusoids 883
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11.2 The Law of Sines 897 minimizes
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11.2 The Law of Sines 899 a angle-s
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11.2 The Law of Sines 901 determine
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11.2 The Law of Sines 903 Let x den
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11.2 The Law of Sines 905 24. Along
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11.2 The Law of Sines 907 33. The a
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11.2 The Law of Sines 909 25. (a)
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11.3 The Law of Cosines 911 of B ar
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11.3 The Law of Cosines 913 the pre
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11.3 The Law of Cosines 915 A 2 = =
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11.3 The Law of Cosines 917 22. A n
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11.4 Polar Coordinates 919 11.4 Pol
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11.4 Polar Coordinates 921 The poin
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11.4 Polar Coordinates 923 4. We mo
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11.4 Polar Coordinates 925 Solution
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11.4 Polar Coordinates 927 Solution
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11.4 Polar Coordinates 929 algebrai
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11.4 Polar Coordinates 931 45. ( )
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11.4 Polar Coordinates 933 5. ( 12,
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11.4 Polar Coordinates 935 13. (
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11.4 Polar Coordinates 937 73. r =7
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11.5 Graphs of Polar Equations 939
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11.6 Hooked on Conics Again 973 11.
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11.6 Hooked on Conics Again 989 2 9
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11.7 Polar Form of Complex Numbers
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11.8 Vectors 1013 Q ′ (1, 7) up 4
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11.8 Vectors 1015 ⃗v + ⃗w = 〈
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11.8 Vectors 1017 ⃗v − ⃗w =
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11.8 Vectors 1019 The remaining pro
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11.8 Vectors 1021 ‖k⃗v‖ = ‖
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11.8 Vectors 1023 at the origin, th
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11.8 Vectors 1025 Geometrically, th
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11.8 Vectors 1027 11.8.1 Exercises
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11.8 Vectors 1029 44. ⃗v = 〈−
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11.8 Vectors 1031 11.8.2 Answers 1.
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11.8 Vectors 1033 47. ‖⃗v‖ =2
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11.9 The Dot Product and Projection
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11.10 Parametric Equations 1049 obj
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11.10 Parametric Equations 1051 2.
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11.10 Parametric Equations 1053 Now
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11.10 Parametric Equations 1061 Sup
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Index n th root of a complex number
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Index 1071 central angle, 701 chang
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Index 1073 reflective property, 523
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Index 1075 matrix, multiplicative,
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Index 1077 midpoint definition of,
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Index 1079 instantaneous, 161, 472
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Index 1081 inconsistent, 553 indepe
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College Trigonometry, 2011a

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