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 45ยฐ, 30ยฐ and 60ยฐ
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 ฮธ = Sin ฮฑ
The Equation Cos ฮธ = Cos ฮฑ
The Equation Tan ฮธ = Tan ฮฑ
Summary of Results
Glossary
Summary of Trigonomeb1c Formulae
Answers
Index