Practice Makes Perfect™ Trigonometry

Sales Handle A no-nonsense practical guide to trigonometry, providing concise summaries, clear model examples, and plenty of practice, making this workbook the ideal complement to class study or self-study, preparation for exams or a brush-up on rusty skills. About the Book Established as a successful practical workbook series with over 30 titles in the language learning category, Practice Makes Perfect now provides the same clear, concise approach and extensive exercises to key fields within mathematics. The key to the Practice Makes Perfect series is the extensive exercises that provide learners with all the practice they need for mastery. Not focused on any particular test or exam, but complementary to most trigonometry curricula Large trim allows clear presentation of worked problems, exercises, and explained answers. Practice on essential trig concepts: sine, cosine, tangent, cotangent, secant and cosecant. Features No-nonsense approach: provides clear presentation of content. Over 500 exercises and answers covering all aspects of trigonometry Successful series:'Practice Makes Perfect'has sales of 1 million+ copies in the language category – now applied to mathematics Market / Audience For students who need to review and practice trigonometry, whether to keep up with class work or to prepare for a test or exam (such as SAT and ACT in the US, or GCSE in the UK). International suitability: High Benefit to the Customer Workbook is not exam specific, yet it provides thorough coverage of the trigonometry skills required in most math tests. About the Authors Carolyn Wheater ( Hawthorne, NJ) teaches middle school and upper school mathematics at the Nightingale-Bamford School in New York City. Educated at Marymount Manhattan College and the University of Massachusetts, Amherst, she has taught math and computer technology for 30 years to students from preschool through college. She is a member of National Council of Teachers of Mathematics (NCTM) and the Association of Teachers in Independent Schools. MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict MuPDF error: syntax error: invalid key in dict Contents 7 Preface 9 1 Right triangle trigonometry 13 Angle measurement: degrees 13 Degrees, minutes, seconds 14 Bearings 14 Angle of elevation and angle of depression 15 Similar triangles 16 Trigonometric ratios 17 Finding sides 19 Finding angles 21 Finding areas 23 2 Trigonometric functions 27 Radian measure 27 Angles in standard position 30 The unit circle 32 Trigonometric functions 34 3 Graphs of trigonometric functions 41 Graphs of sine and cosine functions 41 Shifting, stretching, compressing, and reflecting 44 Graphs of other trigonometric functions 46 Inverse trigonometric functions 49 Graphs of the inverse functions 51 Evaluating inverse functions 52 4 Applications of sinusoidal functions 53 Sinusoidal functions 53 Circular motion 59 Springs and pendulums 61 Rhythms in nature 63 5 Identities and equations 67 Fundamental identities 67 Verifying identities 70 Solving trigonometric equations 72 Sum and difference identities 74 Double-angle and half-angle identities 77 Product-sum and power-reducing identities 81 6 Law of sines and law of cosines 83 The law of sines 83 The law of cosines 90 Solving triangles 94 7 Polar coordinate system 97 Polar coordinates 97 Multiple representations 99 Converting coordinates 102 Polar equations 103 Converting equations 106 8 Complex numbers 109 Graphing complex numbers 109 Arithmetic of complex numbers 111 Rectangular and trigonometric form 114 Multiplication and division 115 Powers and roots 117 9 Vectors in the plane 123 Representing vectors 123 Changing forms 126 Addition of vectors 128 Scalar multiplication 131 Subtraction of vectors 131 Multiplication of vectors 132 Dot products 132 Orthogonal vectors 134 Answer key 137 Contents......Page 7 Preface......Page 9 Angle measurement: degrees......Page 13 Bearings......Page 14 Angle of elevation and angle of depression......Page 15 Similar triangles......Page 16 Trigonometric ratios......Page 17 Finding sides......Page 19 Finding angles......Page 21 Finding areas......Page 23 Radian measure......Page 27 Angles in standard position......Page 30 The unit circle......Page 32 Trigonometric functions......Page 34 Graphs of sine and cosine functions......Page 41 Shifting, stretching, compressing, and reflecting......Page 44 Graphs of other trigonometric functions......Page 46 Inverse trigonometric functions......Page 49 Graphs of the inverse functions......Page 51 Evaluating inverse functions......Page 52 Sinusoidal functions......Page 53 Circular motion......Page 59 Springs and pendulums......Page 61 Rhythms in nature......Page 63 Fundamental identities......Page 67 Verifying identities......Page 70 Solving trigonometric equations......Page 72 Sum and difference identities......Page 74 Double-angle and half-angle identities......Page 77 Product-sum and power-reducing identities......Page 81 The law of sines......Page 83 The law of cosines......Page 90 Solving triangles......Page 94 Polar coordinates......Page 97 Multiple representations......Page 99 Converting coordinates......Page 102 Polar equations......Page 103 Converting equations......Page 106 Graphing complex numbers......Page 109 Arithmetic of complex numbers......Page 111 Rectangular and trigonometric form......Page 114 Multiplication and division......Page 115 Powers and roots......Page 117 Representing vectors......Page 123 Changing forms......Page 126 Addition of vectors......Page 128 Subtraction of vectors......Page 131 Dot products......Page 132 Orthogonal vectors......Page 134 Answer key......Page 137 Don't be tripped up by trigonometry. Master this math with practice, practice, practice! Practice Makes Trigonometry is a comprehensive guide and workbook that covers all the basics of trigonometry that you need to understand this subject. Each chapter focuses on one major topic, with thorough explanations and many illustrative examples, so you can learn at your own pace and really absorb the information. You get to apply your knowledge and practice what you've learned through a variety of exercises, with an answer key for instant feedback. Offering a winning solution for getting a handle on math right away, Practice Makes Trigonometry is your ultimate resource for building a solid understanding of trigonometry fundamentals. Contains explanations of a variety of trigonometry concepts and skills, with more than 700 exercises and answers