Trigonometric Functions And Complex Numbers: In Mathematical Olympiad And Competitions

by Desheng Yang, Chunhui Shen (Translator)

Overview

Trigonometric Functions and Complex Numbers covers the followings areas in the International Mathematical Olympiad (IMO) and other mathematical competitions. The contents are essential for the IMO. A good help for students who want to improve in these areas.

Product Details

ISBN-13:	9781938134760
Publisher:	World Century Publishing Corporation
Publication date:	11/17/2016
Series:	World Century Mathematical Olympiad Series , #1
Pages:	424
Product dimensions:	6.00(w) x 9.00(h) x 0.94(d)

Table of Contents

Preface v

Part I Trigonometric Function 1

Chapter 1 Trigonometric Identity 3

1.1 Trigonometric Ratios for Any Angle 3

1.2 The Induction Formulas and the Relationship Between Trigonometric Ratios of the Same Angle 16

Chapter 2 Trigonometric Identity 33

2.1 Cosines, Sines and Tangents of Addition and Subtraction of Two Angles 33

2.2 Double Angles, Half-Angle, Sum-to-Product Formula and Product-to-Sum Formula 45

Chapter 3 Trigonometric Functions 65

3.1 Graphs and Properties of Trigonometric Functions 65

Chapter 4 Inverse Trigonometric Functions and Trigonometric Equations 97

4.1 Inverse Trigonometric Functions 97

4.2 Trigonometric Equations 110

Chapter 5 Solutions of Triangles 121

5.1 Solutions of Triangles 121

5.2 Area Method 142

Chapter 6 Trigonometric Substitution and Trigonometric Inequality 151

6.1 Trigonometric Substitution 151

6.2 Trigonometric Inequality 161

Part II Complex Number 189

Chapter 7 Concept of Complex Number 191

Chapter 8 Operations with Complex Number 215

8.1 Operations with Complex Number 215

Chapter 9 Trigonometric Form of a Complex Number 227

Chapter 10 Complex Number and Equation 251

Answers 283