Trigonometry: A Complete Introduction

by Hugh Neill

Overview

Trigonometry: A Complete Introduction is the most comprehensive yet easy-to-use introduction to Trigonometry. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge.


The book covers all areas of trigonometry including the theory and equations of tangent, sine and cosine, using trigonometry in three dimensions and for angles for any magnitude, related to triangles. Everything you will need is here in this one book. Each chapter includes not only an explanation of the knowledge and skills you need, but also worked examples and test questions.

Product Details

ISBN-13:	9781473678491
Publisher:	Mobius
Publication date:	09/25/2018
Edition description:	Revised
Pages:	256
Product dimensions:	5.30(w) x 8.40(h) x 0.50(d)

About the Author

Hugh Neill is a maths teacher who has also been an inspector and chief examiner. His books have helped over 100,000 people to improve their mathematics.

Table of Contents

Welcome to Trigonometry: A complete Introduction ix

Introduction xi

1 The tangent 1

1.1 Introduction

1.2 The idea of the tangent ratio

1.3 A definition of tangent

1.4 Values of the tangent

1.5 Notation for angles and sides

1.6 Using tangents

1.7 Opposite and adjacent sides

2 Sine and cosine 15

2.1 Introduction

2.2 Definition of sine and cosine

2.3 Using the sine and cosine

2.4 Trigonometric ratios of 45°, 30° and 60°

2.5 Using the calculator accurately

2.6 Slope and gradient

2.7 Projections

2.8 Multistage problems

3 In three dimensions 33

3.1 Introduction

3.2 Pyramid problems

3.3 Box problems

3.4 Wedge problems

4 Angles of any magnitude 43

4.1 Introduction

4.2 Sine and cosine for any angle

4.3 Graphs of sine and cosine functions

4.4 The tangent of any angle

4.5 Graph of the tangent function

4.6 Sine, cosine and tangent

5 Solving simple equations 53

5.1 Introduction

5.2 Solving equations involving sines

5.3 Solving equations involving cosines

5.4 Solving equations involving tangents

6 The sine and cosine formulae 63

6.1 Notation

6.2 Area of a triangle

6.3 The sine formula for a triangle

6.4 The ambiguous case

6.5 The cosine formula for a triangle

6.6 Introduction to surveying

6.7 Finding the height of a distant object

6.8 Distance of an inaccessible object

6.9 Distance between two inaccessible but visible objects

6.10 Triangulation

7 Radians 87

7.1 Introduction

7.2 Radians

7.3 Length of a circular arc

7.4 Converting from radians to degrees

7.5 Area of a circular sector

8 Relations between the ratios 95

8.1 Introduction

8.2 Secant, cosecant and cotangent

9 Ratios and compound angles 103

9.1 Compound angles

9.2 Formulae for sin(A + B) and sin(A - B)

9.3 Formulae for cos(A + B) and cos(A - B)

9.4 Formulae for tan(A + B) and tan(A - B)

9.5 Worked examples

9.6 Multiple angle formulae

9.7 Identities

9.8 More trigonometric equations

10 The forms a sin x and b cos x 119

10.1 Introduction

10.2 The form y = asin x + bcos x

10.3 Using the alternative form

11 The factor formulae 129

11.1 The first set of factor formulae

11.2 The second set of factor formulae

12 Circles related to triangles 139

12.1 The circumcircle

12.2 The incircle

12.3 The ecircles

12.4 Heron's formula: the area of a triangle

13 General solution of equations 153

13.1 The equation sin θ = sin α

13.2 The equation cos θ = cos α

13.3 The equation tan θ = tan α

Glossary 161

Summary of trigonometric formulae 165

Answers 169

Index 185