The back cover says:

This

study aid is to help the student to master the basic techniques of

solving difficult problems in trigonometry. The book contains

theoretical material, many worked competition problems, and some

problems to be solved independently (the answers being at end of the

book.) Intended for high-school and precollege students.

The

book has some interesting things, for example it introduces the

trigonometric functions as a feature of a trigonometric circle instead

of a right-angled triangle as many books do. Also the second chapter

(Identical Transformations of Trigonometric Expressions) will help you

understand many combination formulae (which we learn by heart in many

cases without understanding). Chapter 4 (Investigating Trigonometric

Functions) treats the trigonometric functions graphically and analyzes

the meaning of graphs, also with help of their derivatives.

The book was translated from the Russian by *Leonid Levant* and was first published by Mir in 1988.

Contents:

From the Authors

Contents

5

**Chapter 1. Definitions and Basic Properties of Trigonometric Functions 9**

1.1. Radian Measure of an Arc. Trigonometric Circle 9

1.2. Definitions of the Basic Trigonometric Functions 18

1.3. Basic Properties of Trigonometric Functions 23

1.4. Solving the Simplest Trigonometric Equations. Inverse Trigonometric Functions 31

Problems 36

**Chapter 2. Identical Transformations of Trigonometric Expressions 41**

2.1. Addition Formulas 41

2.2. Trigonometric Identities for .Double, Triple, and Half Arguments 55

2.3. Solution of Problems Involving Trigonometric Transformations 63

Problems 77

**Chapter 3. Trigonometric Equations and Systems of Equations 80**

3. 1. General 80

3.2. Principal Methods of Solving Trigonometric Equations 87

3.3. Solving Trigonometric Equations and Systems of Equations in Several Unknowns 101

Problems 109

**Chapter 4. Investigating Trigonometric Functions 113**

4.1. Graphs of Basic Trigonometric Functions 113

4.2. Computing Limits 126

4.3. Investigating Trigonometric Functions with the Aid of a Derivative 132

Problems 146

**Chapter 5. Trigonometric Inequalities 149**

5.1. Proving Inequalities Involving Trigonometric Functions 149

5.2. Solving Trigonometric Inequalities 156

Problems 162

Answers 163