Teach Yourself Trigonometry

From the Preface : Teach Yourself Trigonometry has been substantially revised and rewritten to take account of modern needs and recent developments in the subject. It is anticipated that every reader will have access to a scientific calculator which has sines, cosines and tangents, and their inverses. It is also important that the calculator has a memory, so that intermediate results can be stored accurately. No support has been given about how to use the calculator, except in the most general terms. Calculators vary considerably in the keystrokes which they use, and what is appropriate for one calculator may be inappropriate for another. There are many worked examples in the book, with complete, detailed answers to all the questions. At the end of each worked example, you will find the symbol I to indicate that the example has been completed, and what follows is text. Contents ======== Contents Preface 01 - Historical Background Introduction What Is Trigonometry The Origins of Trigonometry 02 - The Tangent Introduction The Idea of the Tangent Ratio A Definition of Tangent Values of the Tangent Notation for angles and Sides Using Tangents Opposite and adjacent Sides 03 - Sine and Cosine Introduction Definition of Sine and Cosine Using the Sine and Cosine Trigonometric Ratios of 45°, 30° and 60° Using the Calculator Accurately Slope and Gradient Projections Multistage Problems 04 - In Three Dimensions Introduction Pyramid Problems Box Problems Wedge Problems 05 - Angles of Any Magnitude Introduction Sine and Cosine for Any Angle Graphs of Sine and Cosine Functions The Tangent of any Angle Graph of the Tangent Function Sine, Cosine and Tangent 06 - Solving Simple Equations Introduction Solving Equations Involving Sines Solving Equations Involving Cosines Solving Equations Involving Tangents 07 - The Sine and Cosine Formulae Notation Area of a Triangle The Sine Formula for a Triangle The Ambiguous Case The Cosine Formula for a Triangle Introduction to Surveying Finding the Height of a Distant Object Distance of an Inaccessible Object Distance Between Two Inaccessible but Visible Objects Triangulation 08 - Radians Introduction Radians Length of a Circular Arc Converting from Radians to Degrees Area of a Circular Sector 09 - Relations Between the Ratios Introduction Secant, Cosecant and Cotangent 10 - Ratios of Compound Angles Compound Angles Formulae for Sin(A + 8) and Sin(A - 8) Formulae for Cos(A + 8) and Cos(A - 8) Formulae for Tan(A + 8) and Tan(A - 8) Worked Examples Multiple angle Formulae Identities More Trigonometric Equations 11 - The Form A Sin(X) + B Cos(X) Introduction The Form Y = A Sin(X) + B Cos(X) Using the Alternative Form 12 - The Factor Formulae The First Set of Factor Formulae The Second Set of Factor Formulae 13 - Circles Related to a Triangle The Circumcircle The Incircle The Ecircles Heron's Formula: The area of a Triangle 14 - General Solution of Equations The Equation Sin θ = Sin α The Equation Cos θ = Cos α The Equation Tan θ = Tan α Summary of Results Glossary Summary of Trigonomeb1c Formulae Answers Index Front Cover......Page 1 Contents......Page 5 Preface......Page 8 01 - Historical Background......Page 9 Introduction......Page 10 The Origins of Trigonometry......Page 11 02 - The Tangent......Page 13 Introduction......Page 14 The Idea of the Tangent Ratio......Page 15 A Definition of Tangent......Page 16 Values of the Tangent......Page 17 Using Tangents......Page 18 Opposite and adjacent Sides......Page 22 03 - Sine and Cosine......Page 26 Introduction......Page 27 Definition of Sine and Cosine......Page 28 Using the Sine and Cosine......Page 29 Trigonometric Ratios of 45°, 30° and 60°......Page 33 Slope and Gradient......Page 35 Projections......Page 36 Multistage Problems......Page 38 04 - In Three Dimensions......Page 43 Pyramid Problems......Page 44 Box Problems......Page 47 Wedge Problems......Page 49 05 - Angles of Any Magnitude......Page 53 Sine and Cosine for Any Angle......Page 54 Graphs of Sine and Cosine Functions......Page 56 The Tangent of any Angle......Page 58 Graph of the Tangent Function......Page 59 Sine, Cosine and Tangent......Page 60 06 - Solving Simple Equations......Page 61 Solving Equations Involving Sines......Page 62 Solving Equations Involving Cosines......Page 65 Solving Equations Involving Tangents......Page 67 07 - The Sine and Cosine Formulae......Page 70 Area of a Triangle......Page 71 The Sine Formula for a Triangle......Page 74 The Ambiguous Case......Page 76 The Cosine Formula for a Triangle......Page 77 Finding the Height of a Distant Object......Page 81 Distance of an Inaccessible Object......Page 83 Triangulation......Page 84 08 - Radians......Page 91 Length of a Circular Arc......Page 92 Converting from Radians to Degrees......Page 94 Area of a Circular Sector......Page 95 09 - Relations Between the Ratios......Page 98 Secant, Cosecant and Cotangent......Page 99 10 - Ratios of Compound Angles......Page 104 Formulae for Sin(A + 8) and Sin(A - 8)......Page 105 Formulae for Cos(A + 8) and Cos(A - 8)......Page 107 Formulae for Tan(A + 8) and Tan(A - 8)......Page 108 Worked Examples......Page 109 Multiple angle Formulae......Page 111 Identities......Page 114 More Trigonometric Equations......Page 116 11 - The Form A Sin(X) + B Cos(X)......Page 118 The Form Y = A Sin(X) + B Cos(X)......Page 119 Using the Alternative Form......Page 122 12 - The Factor Formulae......Page 126 The First Set of Factor Formulae......Page 127 The Second Set of Factor Formulae......Page 130 13 - Circles Related to a Triangle......Page 134 The Circumcircle......Page 135 The Incircle......Page 139 The Ecircles......Page 140 Heron's Formula: The area of a Triangle......Page 142 14 - General Solution of Equations......Page 146 The Equation Sin θ = Sin α......Page 147 The Equation Tan θ = Tan α......Page 149 Summary of Results......Page 150 Glossary......Page 153 Summary of Trigonomeb1c Formulae......Page 156 Answers......Page 159 Index......Page 171 Back Cover......Page 176

teach Yourself Trigonometry is Suitable For Beginners, But It Also Goes Beyond The Basics To Offer Comprehensive Coverage Of More Advanced Topics. Each Chapter Features Numerous Worked Examples And Many Carefully Graded Exercises, And Full Demonstrations Of Trigonometric Proofs Are Given In The Answer Key.