Teach Yourself Trigonometry

✍ Scribed by P. Abbott

• Publisher: McGraw-Hill
• Year: 2003
• Tongue: English
• Leaves: 176
• Edition: 2
• Category: Library

✦ Synopsis

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

✦ Table of Contents

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