Teach Yourself Trigonometry

Description

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