College Trigonometry, 2011a

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ii Acknowledgements While the cover of this textbook lists only two names, the book as it stands today would simply not exist if not for the tireless work and dedication of several people. First and foremost, we wish to thank our families for their patience and support during the creative process. We would also like to thank our students - the sole inspiration for the work. Among our colleagues, we wish to thank Rich Basich, Bill Previts, and Irina Lomonosov, who not only were early adopters of the textbook, but also contributed materials to the project. Special thanks go to Katie Cimperman, Terry Dykstra, Frank LeMay, and Rich Hagen who provided valuable feedback from the classroom. Thanks also to David Stumpf, Ivana Gorgievska, Jorge Gerszonowicz, Kathryn Arocho, Heather Bubnick, and Florin Muscutariu for their unwaivering support (and sometimes defense) of the book. From outside the classroom, we wish to thank Don Anthan and Ken White, who designed the electric circuit applications used in the text, as well as Drs. Wendy Marley and Marcia Ballinger for the Lorain CCC enrollment data used in the text. The authors are also indebted to the good folks at our schools’ bookstores, Gwen Sevtis (Lakeland CC) and Chris Callahan (Lorain CCC), for working with us to get printed copies to the students as inexpensively as possible. We would also like to thank Lakeland folks Jeri Dickinson, Mary Ann Blakeley, Jessica Novak, and Corrie Bergeron for their enthusiasm and promotion of the project. The administrations at both schools have also been very supportive of the project, so from Lakeland, we wish to thank Dr. Morris W. Beverage, Jr., President, Dr. Fred Law, Provost, Deans Don Anthan and Dr. Steve Oluic, and the Board of Trustees. From Lorain County Community College, we wish to thank Dr. Roy A. Church, Dr. Karen Wells, and the Board of Trustees. From the Ohio Board of Regents, we wish to thank former Chancellor Eric Fingerhut, Darlene McCoy, Associate Vice Chancellor of Affordability and Efficiency, and Kelly Bernard. From OhioLINK, we wish to thank Steve Acker, John Magill, and Stacy Brannan. We also wish to thank the good folks at WebAssign, most notably Chris Hall, COO, and Joel Hollenbeck (former VP of Sales.) Last, but certainly not least, we wish to thank all the folks who have contacted us over the interwebs, most notably Dimitri Moonen and Joel Wordsworth, who gave us great feedback, and Antonio Olivares who helped debug the source code.
Table of Contents vii 10 Foundations of Trigonometry 693 10.1 Angles and their Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693 10.1.1 Applications of Radian Measure: Circular Motion . . . . . . . . . . . . . . 706 10.1.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 709 10.1.3 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712 10.2 The Unit Circle: Cosine and Sine . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717 10.2.1 Beyond the Unit Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 730 10.2.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736 10.2.3 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 740 10.3 The Six Circular Functions and Fundamental Identities . . . . . . . . . . . . . . . . 744 10.3.1 Beyond the Unit Circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 752 10.3.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759 10.3.3 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 766 10.4 Trigonometric Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 770 10.4.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782 10.4.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787 10.5 Graphs of the Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . 790 10.5.1 Graphs of the Cosine and Sine Functions . . . . . . . . . . . . . . . . . . . 790 10.5.2 Graphs of the Secant and Cosecant Functions . . . . . . . . . . . . . . . . 800 10.5.3 Graphs of the Tangent and Cotangent Functions . . . . . . . . . . . . . . . 804 10.5.4 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 809 10.5.5 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 811 10.6 The Inverse Trigonometric Functions . . . . . . . . . . . . . . . . . . . . . . . . . . 819 10.6.1 Inverses of Secant and Cosecant: Trigonometry Friendly Approach . . . . . 827 10.6.2 Inverses of Secant and Cosecant: Calculus Friendly Approach . . . . . . . . 830 10.6.3 Calculators and the Inverse Circular Functions. . . . . . . . . . . . . . . . . 833 10.6.4 Solving Equations Using the Inverse Trigonometric Functions. . . . . . . . 838 10.6.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 841 10.6.6 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 849 10.7 Trigonometric Equations and Inequalities . . . . . . . . . . . . . . . . . . . . . . . 857 10.7.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874 10.7.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877 11 Applications of Trigonometry 881 11.1 Applications of Sinusoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 881 11.1.1 Harmonic Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885 11.1.2 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 891 11.1.3 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894 11.2 The Law of Sines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896 11.2.1 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 904 11.2.2 Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 908 11.3 The Law of Cosines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 910
Page 1: College Trigonometry Version ⌊π
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
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30 ◦ 1 10.2 The Unit Circle: Cosi
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10.2 The Unit Circle: Cosine and Si
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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 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 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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