College Trigonometry, 2011a

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1046 Applications of <strong>Trigonometry</strong> 11. ⃗v = 〈−8, 3〉 and ⃗w = 〈2, 6〉 ⃗v · ⃗w =2 θ ≈ 87.88 ◦ proj ⃗w (⃗v) = 〈 1 10 , 3 〉 10 ⃗q = 〈 − 81 10 , 27 〉 10 13. ⃗v =3î − ĵ and ⃗w =4ĵ ⃗v · ⃗w = −4 θ ≈ 108.43 ◦ proj ⃗w (⃗v) =〈0, −1〉 ⃗q = 〈3, 0〉 15. ⃗v = 3 2î + 3 2ĵ and ⃗w =î − ĵ ⃗v · ⃗w =0 θ =90 ◦ proj ⃗w (⃗v) =〈0, 0〉 ⃗q = 〈 3 2 , 3 〉 2 〈 √ 〉 17. ⃗v = 1 2 , 3 and ⃗w = ⃗v · ⃗w = θ =75 ◦ 2 √ √ 6− 2 4 〈 √ 1− 3 4 , proj ⃗w (⃗v) = 〈 √ 〉 ⃗q = 1+ 3 4 , 1+√ 3 4 19. ⃗v = 〈 √3 2 , 1 2 〉 and ⃗w = √ √ ⃗v · ⃗w = − 6+ 2 4 θ = 165 ◦ proj ⃗w (⃗v) = ⃗q = 〈 √3+1 4 , 〈 √3−1 〉 4 , 1−√ 3 4 〈 √ √ 〉 − 2 2 , 2 2 √ 〉 3−1 4 〈 √ √ 〉 − 2 2 , − 2 2 √ 〉 3+1 4 12. ⃗v = 〈34, −91〉 and ⃗w = 〈0, 1〉 ⃗v · ⃗w = −91 θ ≈ 159.51 ◦ proj ⃗w (⃗v) =〈0, −91〉 ⃗q = 〈34, 0〉 14. ⃗v = −24î +7ĵ and ⃗w =2î ⃗v · ⃗w = −48 θ ≈ 163.74 ◦ proj ⃗w (⃗v) =〈−24, 0〉 ⃗q = 〈0, 7〉 16. ⃗v =5î +12ĵ and ⃗w = −3î +4ĵ ⃗v · ⃗w =33 θ ≈ 59.49 ◦ proj ⃗w (⃗v) = 〈 − 99 25 , 132 〉 25 ⃗q = 〈 224 25 , 168 〉 25 18. ⃗v = ⃗v · ⃗w = 〈 √2 √ 2 , 2 2 √ √ 2− 6 4 θ = 105 ◦ proj ⃗w (⃗v) = ⃗q = 〈 3 √ 2+ √ 6 8 , 〉 and ⃗w = 〈 √2− √ 6 8 , 3√ 2− √ 6 8 √ √ 〉 2+ 6 8 〈 √ 〉 20. ⃗v = 1 2 , − 3 and ⃗w = ⃗v · ⃗w = θ =15 ◦ 2 √ 6+ √ 2 4 〈 √3+1 proj ⃗w (⃗v) = 4 , − 〈 √ 〉 ⃗q = 1− 3 4 , 1−√ 3 4 〈 √ 〉 1 2 , − 3 2 〈 √2 √ 〉 3+1 4 〉 √ 2 , − 2 2 〉 21. (1500 pounds)(300 feet) cos (0 ◦ ) = 450, 000 foot-pounds 22. (10 pounds)(3 feet) cos (0 ◦ ) = 30 foot-pounds
11.9 The Dot Product and Projection 1047 23. (13 pounds)(25 feet) cos (15 ◦ ) ≈ 313.92 foot-pounds 24. (100 pounds)(42 feet) cos (13 ◦ ) ≈ 4092.35 foot-pounds 25. (200 pounds)(10 feet) cos (77.5 ◦ ) ≈ 432.88 foot-pounds
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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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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 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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11.7 Polar Form of Complex Numbers
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11.7 Polar Form of Complex Numbers
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College Trigonometry, 2011a

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