College Trigonometry, 2011a

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856 Foundations of <strong>Trigonometry</strong> 208. 36.87 ◦ and 53.13 ◦ 209. 22.62 ◦ and 67.38 ◦ 210. 32.52 ◦ and 57.48 ◦ 211. 68.9 ◦ 212. 7.7 ◦ 213. 51 ◦ 214. 19.5 ◦ 215. 41.81 ◦ ( ( )) 12 216. f(x) =5sin(3x) + 12 cos(3x) = 13 sin 3x + arcsin ≈ 13 sin(3x +1.1760) 13 ( ( 3 217. f(x) =3cos(2x)+4sin(2x) =5sin 2x + arcsin ≈ 5sin(2x +0.6435) 5)) 218. f(x) = cos(x) − 3sin(x) = √ ( ( )) 10 sin x + arccos − 3√ 10 ≈ √ 10 sin(x +2.8198) 10 ( ( 219. f(x) =7sin(10x) − 24 cos(10x) = 25 sin 10x + arcsin − 24 )) ≈ 25 sin(10x − 1.2870) 25 220. f(x) =− cos(x) − 2 √ ( ( 1 2sin(x) =3sin x + π + arcsin ≈ 3sin(x +3.4814) 3)) 221. f(x) =2sin(x) − cos(x) = √ ( ( √ )) 5 5sin x + arcsin − ≈ √ 5sin(x − 0.4636) 5 222. 224. [ − 1 5 , 1 ] 5 [ √ √ ] 2 2 − 2 , 2 223. [− 1 3 , 1 ] 225. (−∞, − √ 5] ∪ [− √ 3, √ 3] ∪ [ √ 5, ∞) 226. (−∞, ∞) 227. (−∞, −3) ∪ (−3, 3) ∪ (3, ∞) ( ) [ ) 1 1 228. 2 , ∞ 229. 2 , ∞ 230. ( −∞, − 1 ] [ ) 1 ∪ 12 12 , ∞ 232. (−∞, −2] ∪ [2, ∞) 233. [0, ∞) 231. (−∞, −6] ∪ [−4, ∞)
10.7 Trigonometric Equations and Inequalities 857 10.7 Trigonometric Equations and Inequalities In Sections 10.2, 10.3 and most recently 10.6, we solved some basic equations involving the trigonometric functions. Below we summarize the techniques we’ve employed thus far. Note that we use the neutral letter ‘u’ as the argument 1 of each circular function for generality. Strategies for Solving Basic Equations Involving Trigonometric Functions ˆ To solve cos(u) =c or sin(u) =c for −1 ≤ c ≤ 1, first solve for u in the interval [0, 2π) and add integer multiples of the period 2π. Ifc1, there are no real solutions. ˆ To solve sec(u) =c or csc(u) =c for c ≤−1orc ≥ 1, convert to cosine or sine, respectively, and solve as above. If −1
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College Trigonometry Version ⌊π
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Table of Contents vii 10 Foundation
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Preface Thank you for your interest
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xi text and we have gone to great l
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Chapter 10 Foundations of Trigonome
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10.1 Angles and their Measure 695 k
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10.1 Angles and their Measure 697 2
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10.1 Angles and their Measure 701 T
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10.1 Angles and their Measure 703 y
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10.1 Angles and their Measure 705 y
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10.1 Angles and their Measure 707 h
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10.1 Angles and their Measure 711 I
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10.2 The Unit Circle: Cosine and Si
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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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Page 197 and 198: Chapter 11 Applications of Trigonom
Page 199 and 200: 11.1 Applications of Sinusoids 883
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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 975 Exa
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11.6 Hooked on Conics Again 977 The
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11.6 Hooked on Conics Again 979 We
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11.6 Hooked on Conics Again 983 The
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11.6 Hooked on Conics Again 985 In
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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 1057 Our
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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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