Bruce / Langford / Maxwell Analytic Trigonometry

The Commonwealth and International Library of Science, Technology, Engineering and Liberal Studies: Mathematics Division
1. Auflage 2014
ISBN: 978-1-4831-8064-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 358 Seiten, Web PDF

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.

Autoren/Hrsg.

Bruce, William J.

Langford, W. J.

Maxwell, E. A.

Sneddon, I. N.

Inhaltsverzeichnis

1;Front Cover;1
2;Analytic Trigonometry;4
3;Copyright Page;5
4;Table of Contents;10
5;PREFACE;6
6;THE GREEK ALPHABET;9
7;CHAPTER 1. FOUNDATIONS;16
7.1;1.1. Essential Elements from Algebra;16
7.2;1.2. Essential Elements from Plane Geometry;21
7.3;1.3. Essential Elements from Analytic Geometry;24
8;CHAPTER 2. TRIGONOMETRIC FUNCTIONS OF ANGLES;29
8.1;2.1. Angles;29
8.2;2.2. Definitions of the Trigonometric Functions;30
8.3;2.3. Graphs of the Trigonometric Functions;32
8.4;2.4. Interdependence of the Functions;37
8.5;2.5. Algebraic Equivalents of the Functions;40
8.6;2.6. Elementary Identities;43
8.7;2.7. Functions of Special Angles;46
8.8;2.8. Functions Determined from a Known Function;50
8.9;2.9. Tables of Trigonometric Functions;53
8.10;2.10. Interpolation;54
8.11;2.11. Solutions of Elementary Trigonometric Equations;55
9;CHAPTER 3. FUNCTIONS OF SUMS AND RELATED FUNCTIONS;61
9.1;3.1. Functions of Sums;62
9.2;3.2. Functions of Multiple Angles;69
9.3;3.3. Conversion Formulas for Sums and Products;73
9.4;3.4. Graphical Reduction;75
10;CHAPTER 4. TRIGONOMETRIC FUNCTIONS OF A NUMBER;80
10.1;4.1. Definitions of the Trigonometric Functions of a Number;80
10.2;4.2. Tables of Trigonometric Functions of Numbers;83
10.3;4.3. Solutions of Equations—Approximation Methods;85
11;CHAPTER 5. INVERSE TRIGONOMETRIC FUNCTIONS;89
11.1;5.1. Definitions of the Inverse Trigonometric Functions;89
11.2;5.2. Graphs of the Inverse Trigonometric Functions;91
11.3;5.3. Identities of Inverse Trigonometric Functions;94
11.4;5.4. Equations of Inverse Trigonometric Functions;95
11.5;5.5. General Solutions of Trigonometric Equations;97
12;CHAPTER 6. SKETCHING GRAPHS OF TRIGONOMETRIC FUNCTIONS;102
12.1;6.1. Sketching from the Unit Circle;102
12.2;6.2. Change of Amplitude and Period;106
12.3;6.3. Translation;112
12.4;6.4. Addition of Ordinates;116
12.5;6.5. The Forms k sin (. ± .) and k cos (. ± .);119
12.6;6.6. Graphs of Products;125
13;CHAPTER 7. LOGARITHMS;129
13.1;7.1. The Logarithm Function;129
13.2;7.2. Laws of Logarithms;132
13.3;7.3. Common or Briggsian Logarithms;134
13.4;7.4. Reading Tables of Mantissas;135
13.5;7.5. Interpolation;136
13.6;7.6. Logarithms of Trigonometric Functions;138
14;CHAPTER 8. SOLUTIONS OF TRIANGLES;141
14.1;8.1. The Right Triangle;141
14.2;8.2. Vectors;148
14.3;8.3. The Law of Sines;154
14.4;8.4. The Law of Cosines;160
14.5;8.5. Other Useful Formulas;163
15;CHAPTER 9. POLAR COORDINATES;167
15.1;9.1. The Polar Coordinate System;167
15.2;9.2. Functions in Polar Coordinates;170
15.3;9.3. Elementary Polar Curves;176
15.4;9.4. Aids in Sketching Polar Curves;180
15.5;9.5. Intersections of Polar Curves;185
16;CHAPTER 10. COMPLEX NUMBERS;188
16.1;10.1. Rectangular Form;188
16.2;10.2. Polar Form;191
16.3;10.3. The Fundamental Operations;193
16.4;10.4. De Moivre's Theorem;195
16.5;10.5. Series Representation;198
16.6;10.6. Euler's Formula;202
17;SUPPLEMENT;206
17.1;Analysis of the Definitions of the Trigonometric Functions;206
18;ANSWERS;237
19;TABLES;246
19.1;I. Squares and Square Roots of Numbers;248
19.2;II. Common Logarithms of Numbers;253
19.3;III. Trigonometric Functions of Angles;271
19.4;IV. Logarithms of the Trigonometric Functions of Angles;294
19.5;V. Trigonometric Functions of Numbers;339
20;INDEX;356