College Trigonometry, 2011a

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854 Foundations of <strong>Trigonometry</strong> 172. cos (2 arctan (x)) = 1 − x2 for all x 1+x2 173. sin(arccos(2x)) = √ 1 − 4x 2 for − 1 2 ≤ x ≤ 1 2 ( ( x )) √ 25 − x 2 174. sin arccos = for −5 ≤ x ≤ 5 5 5 ( ( x )) √ 4 − x 2 175. cos arcsin = for −2 ≤ x ≤ 2 2 2 176. cos (arctan (3x)) = 1 √ 1+9x 2 for all x 177. sin(2 arcsin(7x)) = 14x √ 1 − 49x 2 for − 1 7 ≤ x ≤ 1 7 ( ( x √ )) 3 178. sin 2 arcsin = 2x√ 3 − x 2 for − √ 3 ≤ x ≤ √ 3 3 3 179. cos(2 arcsin(4x)) = 1 − 32x 2 for − 1 4 ≤ x ≤ 1 4 180. sec(arctan(2x)) tan(arctan(2x)) = 2x √ 1+4x 2 for all x 181. sin (arcsin(x) + arccos(x)) = 1 for −1 ≤ x ≤ 1 √ 1 − x 182. cos (arcsin(x) + arctan(x)) = 2 − x 2 √ for −1 ≤ x ≤ 1 1+x 2 ( 183. 10 tan (2 arcsin(x)) = 2x√ √ ) ( √ √ ) (√ ) 1 − x 2 2 2 2 2 1 − 2x 2 for x in −1, − ∪ − 2 2 , ∪ 2 2 , 1 ( ) 1 184. sin 2 arctan(x) = ⎧ ⎪⎨ ⎪⎩ − √ √x 2 +1− 1 2 √ x 2 +1 √ √x 2 +1− 1 2 √ x 2 +1 for x ≥ 0 for x
10.6 The Inverse Trigonometric Functions 855 187. If sec(θ) = x 4 for 0
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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
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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 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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