# Analytic Trigonometry

## 1st Edition

### The Commonwealth and International Library of Science, Technology, Engineering and Liberal Studies: Mathematics Division

**Authors:**William J. Bruce

**Editors:**W. J. Langford E. A. Maxwell I. N. Sneddon

**eBook ISBN:**9781483180649

**Imprint:**Pergamon

**Published Date:**1st January 1963

**Page Count:**358

## Description

Analytic Trigonometry details the fundamental concepts and underlying principle of analytic geometry. The title aims to address the shortcomings in the instruction of trigonometry by considering basic theories of learning and pedagogy. The text first covers the essential elements from elementary algebra, plane geometry, and analytic geometry. Next, the selection tackles the trigonometric functions of angles in general, basic identities, and solutions of equations. The text also deals with the trigonometric functions of real numbers. The fifth chapter details the inverse trigonometric functions, while the sixth chapter covers the procedures for sketching graphs of trigonometric functions. The coverage of the selection also includes logarithm, solutions of triangles, polar coordinates, and complex numbers. The book will be of great use to both instructors and students of trigonometry.

## Table of Contents

Preface

The Greek Alphabet

I Foundations

1.1. Essential Elements from Algebra

1.2. Essential Elements from Plane Geometry

1.3. Essential Elements from Analytic Geometry

II Trigonometric Functions of Angles

2.1. Angles

2.2. Definitions of the Trigonometric Functions

2.3. Graphs of the Trigonometric Functions

2.4. Interdependence of the Functions

2.5. Algebraic Equivalents of the Functions

2.6. Elementary Identities

2.7. Functions of Special Angles

2.8. Functions Determined from a Known Function

2.9. Tables of Trigonometric Functions

2.10. Interpolation

2.11. Solutions of Elementary Trigonometric Equations

III Functions of Sums and Related Functions

3.1. Functions of Sums

3.2. Functions of Multiple Angles

3.3. Conversion Formulas for Sums and Products

3.4. Graphical Reduction

IV Trigonometric Functions of a Number

4.1. Definitions of the Trigonometric Functions of a Number

4.2. Tables of Trigonometric Functions of Numbers

4.3. Solutions of Equations—Approximation Methods

V Inverse Trigonometric Functions

5.1. Definitions of the Inverse Trigonometric Functions

5.2. Graphs of the Inverse Trigonometric Functions

5.3. Identities of Inverse Trigonometric Functions

5.4. Equations of Inverse Trigonometric Functions

5.5. General Solutions of Trigonometric Equations

VI Sketching Graphs of Trigonometric Functions

6.1. Sketching from the Unit Circle

6.2. Change of Amplitude and Period

6.3. Translation

6.4. Addition of Ordinates

6.5. The Forms k sin (θ ± λ) and k cos {θ ± λ)

6.6. Graphs of Products

VII Logarithms

7.1. The Logarithm Function

7.2. Laws of Logarithms

7.3. Common or Briggsian Logarithms

7.4. Reading Tables of Mantissas

7.5. Interpolation

7.6. Logarithms of Trigonometric Functions

VIII Solutions of Triangles

8.1. The Right Triangle

8.2. Vectors

8.3. The Law of Sines

8.4. The Law of Cosines

8.5. Other Useful Formulas

IX Polar Coordinates

9.1. The Polar Coordinate System

9.2. Functions in Polar Coordinates

9.3. Elementary Polar Curves

9.4. Aids in Sketching Polar Curves

9.5. Intersections of Polar Curves

X Complex Numbers

10.1. Rectangular Form

10.2. Polar Form

10.3. The Fundamental Operations

10.4. De Moivre's Theorem

10.5. Series Representation

10.6. Euler's Formula

Supplement

Analysis of the Definitions of the Trigonometric Functions

Answers

Tables

I. Squares and Square Roots of Numbers

II. Common Logarithms of Numbers

III. Trigonometric Functions of Angles

IV. Logarithms of the Trigonometric Functions of Angles

V. Trigonometric Functions of Numbers

Index

## Details

- No. of pages:
- 358

- Language:
- English

- Copyright:
- © Pergamon 1963

- Published:
- 1st January 1963

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483180649