Heavenly mathematics : the forgotten art of spherical trigonometry

Glen Van Brummelen

Princeton University Press |  2012 | 215 páginas | rar - pdf | 4 Mb

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Spherical trigonometry was at the heart of astronomy and ocean-going navigation for two millennia. The discipline was a mainstay of mathematics education for centuries, and it was a standard subject in high schools until the 1950s. Today, however, it is rarely taught. Heavenly Mathematics traces the rich history of this forgotten art, revealing how the cultures of classical Greece, medieval Islam, and the modern West used spherical trigonometry to chart the heavens and the Earth. Glen Van Brummelen explores this exquisite branch of mathematics and its role in ancient astronomy, geography, and cartography; Islamic religious rituals; celestial navigation; polyhedra; stereographic projection; and more. He conveys the sheer beauty of spherical trigonometry, providing readers with a new appreciation for its elegant proofs and often surprising conclusions.

Heavenly Mathematics is illustrated throughout with stunning historical images and informative drawings and diagrams that have been used to teach the subject in the past. This unique compendium also features easy-to-use appendixes as well as exercises at the end of each chapter that originally appeared in textbooks from the eighteenth to the early twentieth centuries.

Contents
Preface vii

1 Heavenly Mathematics 1
2 Exploring the Sphere 23
3 The Ancient Approach 42
4 The Medieval Approach 59
5 The Modern Approach: Right- Angled Triangles 73
6 The Modern Approach: Oblique Triangles 94
7 Areas, Angles, and Polyhedra 110
8 Stereographic Projection 129
9 Navigating by the Stars 151
Appendix A. Ptolemy’s Determination of the Sun’s Position 173
Appendix B. Textbooks 179
Appendix C. Further Reading 182
Index 189

Help Your Kids with Math: A visual problem solver for kids and parents

 

Barry Lewis

DK Publishing | 2010 | 258 páginas | rar - pdf | 9,7 Mb

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Studying math is often a source of great anxiety for children and also proves troublesome for parents helping with their homework.

Using uniquely accessible illustrated stress-free approach, Help Your Kids with Math looks at every aspect of math, from simple sums to simultaneous equations, and explains each facet in easily understandable language so that adults and kids can master the subject together.

In Help Your Kids with Math tricky concepts are explored and examined step-by-step, so that even the most math-phobic individual will be able to approach and solve complex problems with confidence.

Contents
NUMBERS
Introducing numbers ; Addition ; Subtraction ; Multiplication ; Division ; Prime numbers ; Units of measurement ; Positive and negative numbers ; Powers and roots ; Standard form ; Decimals in action; Fractions, Ratio and proportion, Percentages, Converting fractions, decimals, and percentages ; Mental math ; Rounding off ; Using a calculator ; Personal finance ; Business finance
GEOMETRY
What is geometry?; Angles; Straight lines; Symmetry; Coordinates; Vectors; Translations ; Rotations; Reflections; Enlargements; Scale drawings; Bearings; Constructions; Loci ; Triangles; Constructing triangles; Congruent triangles; Area of a triangle; Similar triangles ; Pythagorean Theorem ; Quadrilaterals; Polygons ; Circles ; Circumference and diameter ; Area of a circle ; Angles in a circle; Chords and cyclic quadrilaterals ; Tangents ; Arcs ; Sectors ; Solids ; Volumes ; Surface area 148
TRIGONOMETRY
What is trigonometry? ; Working with trigonometry ; Finding missing sides ; Finding missing angles 
ALGEBRA
What is algebra?; Sequences; Working with expressions; Expanding and factorizing expressions; Quadratic expressions; Formulas; Solving equations; Linear graphs; Simultaneous equations; Factorizing quadratic equations; The quadratic formula; Quadratic graphs ; Inequalities 
STATISTICS
What is statistics? ; Collecting and organizing data ; Bar charts ; Pie charts ; Line graphs;  Averages; Moving Averages ; Measuring spread ; Histograms ; Scatter diagrams 
PROBABILITY
What is probability? , Expectation and reality ; Multiple probability ; Dependent events ; Tree diagrams 
Reference section 232
Glossary 244
Index 252
Acknowledgments 256

Mathematical Connections: A Companion for Teachers

(Classroom Resource Material) 

Al Cuoco

The Mathematical Association of America | 2005 | 261 páginas | pdf | 6,3 Mb

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This book is about some of the topics that form the foundations for high school mathematics. It focuses on a closely-knit collection of ideas that are at the intersection of algebra, arithmetic, combinatorics, geometry, and calculus. Most of the ideas are classical: methods for fitting polynomial functions to data, for summing powers of integers, for visualizing the iterates of a function defined on the complex plane, or for obtaining identities among entries in Pascal's triangle. Some of these ideas, previously considered quite advanced, have become tractable because of advances in computational technology. Others are just beautiful classical mathematics, topics that have fallen out of fashion and that deserve to be resurrected While the book will appeal to many audiences, one of the primary audiences is high school teachers, both practicing and prospective. It can be used as a text for undergraduate or professional courses, and the design lends itself to self-study. Of course, good mathematics for teaching is also good for many other uses, so readers of all persuasions can enjoy exploring some of the beautiful ideas presented in the pages of this book.

Contents
1. Difference tables and polynomial fits. Doing it with sums
Doing it with differences
Finding a formula: combinatorial polynomials
Making it formal: the [delta] operator
Going the other way: polynomials to tables
Conversions
From Newton to Lagrange
Agreeing to disagree
2. Form and function: the algebra of polynomials. Polynomials
The basic theorems
Coefficients and values
Up a level
Transformations
Coefficients and zeros.
3. Complex numbers, complex maps, and trigonometry. Complex numbers
The complex plane
The geometry behind multiplying
Trigonometric identities
Complex maps
Julia sets and the Mandelbrot set.
4. Combinations and locks. Combinatorial proofs and identities
The simplex lock
Some approaches to the simplex lock problem
Connections to the Mahler basis.
5. Sums of powers. Summatory polynomials
Bernoulli's method.

Trigonometry For Dummies

Mary Jane Sterling

 For Dummies | 2014 - 2ª edição | 387 páginas | rar - pdf | 4 Mb


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A plain-English guide to the basics of trig

Trigonometry deals with the relationship between the sides and angles of triangles... mostly right triangles. In practical use, trigonometry is a friend to astronomers who use triangulation to measure the distance between stars. Trig also has applications in fields as broad as financial analysis, music theory, biology, medical imaging, cryptology, game development, and seismology.

From sines and cosines to logarithms, conic sections, and polynomials, this friendly guide takes the torture out of trigonometry, explaining basic concepts in plain English and offering lots of easy-to-grasp example problems. It also explains the "why" of trigonometry, using real-world examples that illustrate the value of trigonometry in a variety of careers.

• Tracks to a typical Trigonometry course at the high school or college level

• Packed with example trig problems

• From the author of Trigonometry Workbook For Dummies

Trigonometry For Dummies is for any student who needs an introduction to, or better understanding of, high-school to college-level trigonometry.

Contents at a Glance

Introduction........ 1

Part I: Getting Started with Trigonometry......... 5

Chapter 1: Trouncing Trig Technicalities..........7

Chapter 2: Coordinating Your Efforts with Cartesian Coordinates...29

Chapter 3: Functioning Well...............47

Chapter 4: Getting Your Degree.............57

Chapter 5: Dishing Out the Pi: Radians.........67

Chapter 6: Getting It Right with Triangles...........81

Part II: Trigonometric Functions........... 91

Chapter 7: Doing Right by Trig Functions..................93

Chapter 8: Trading Triangles for Circles: Circular Functions....109

Chapter 9: Defining Trig Functions Globally........121

Chapter 10: Applying Yourself to Trig Functions............135

Part III: Identities...... 155

Chapter 11: Identifying Basic Identities.......157

Chapter 12: Operating on Identities..........171

Chapter 13: Proving Identities: The Basics..........189

Chapter 14: Sleuthing Out Identity Solutions.........207

Part IV: Equations and Applications........ 223

Chapter 15: Investigating Inverse Trig Functions........225

Chapter 16: Making Inverse Trig Work for You.....233

Chapter 17: Solving Trig Equations........243

Chapter 18: Obeying the Laws.........265

Part V: The Graphs of Trig Functions..... 289

Chapter 19: Graphing Sine and Cosine...........291

Chapter 20: Graphing Tangent and Cotangent........307

Chapter 21: Graphing Other Trig Functions.......317

Chapter 22: Topping Off Trig Graphs........329
Part VI: The Part of Tens.................. 343
Chapter 23: Ten Basic Identities . . . Plus Some Bonuses....345
Chapter 24: Ten Not-So-Basic Identities............349
Appendix: Trig Functions Table......... 353
Index........ 357

Livro relacionado:

Trigonometry workbook for dummies por Mary Jane Sterling Idioma: Inglês   Editora: Hoboken, N.J. ; [Great Britain] : Wiley, ©2005.

Journey through Mathematics Creative Episodes in Its History

Enrique A. González-Velasco

Springer | 2011| 478 páginas | pdf | 4,4 Mb

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This book offers an accessible and in-depth look at some of the most  important episodes of two thousand years of mathematical history. Beginning with trigonometry and moving on through logarithms, complex numbers, infinite series, and calculus, this book profiles some of the lesser known but crucial contributors to modern day mathematics. It is unique in its use of primary sources as well as its accessibility; a knowledge of first-year calculus is the only prerequisite. But undergraduate and graduate students alike will appreciate this glimpse into the fascinating process of mathematical creation.

The history of math is an intercontinental journey, and this book showcases brilliant mathematicians from Greece, Egypt, and India, as well as Europe and the Islamic world. Several of the primary sources have never before been translated into English. Their interpretation is thorough and readable, and offers an excellent background for teachers of high school mathematics as well as anyone interested in the history of math.

TABLE OF CONTENTS
Preface ix
1 TRIGONOMETRY 1
1.1 The Hellenic Period 1
1.2 Ptolemy’s Table of Chords 10
1.3 The Indian Contribution 25
1.4 Trigonometry in the Islamic World 34
1.5 Trigonometry in Europe 55
1.6 From Viète to Pitiscus 65
2 LOGARITHMS 78
2.1 Napier’s First Three Tables 78
2.2 Napier’s Logarithms 88
2.3 Briggs’ Logarithms 101
2.4 Hyperbolic Logarithms 117
2.5 Newton’s Binomial Series 122
2.6 The Logarithm According to Euler 136
3 COMPLEX NUMBERS 148
3.1 The Depressed Cubic 148
3.2 Cardano’s Contribution 150
3.3 The Birth of Complex Numbers 160
3.4 Higher-Order Roots of Complex Numbers 173
3.5 The Logarithms of Complex Numbers 181
3.6 Caspar Wessel’s Breakthrough 185
3.7 Gauss and Hamilton Have the Final Word 190
4 INFINITE SERIES 195
4.1 The Origins 195
4.2 The Summation of Series 203
4.3 The Expansion of Functions 212
4.4 The Taylor and Maclaurin Series 220
5 THE CALCULUS 230
5.1 The Origins 230
5.2 Fermat’s Method of Maxima and Minima 234
5.3 Fermat’s Treatise on Quadratures 248
5.4 Gregory’s Contributions 258
5.5 Barrow’s Geometric Calculus 275
5.6 From Tangents to Quadratures 283
5.7 Newton’s Method of Infinit Series 289
5.8 Newton’s Method of Fluxions 294
5.9 Was Newton’s Tangent Method Original? 302
5.10 Newton’s First and Last Ratios 306
5.11 Newton’s Last Version of the Calculus 312
5.12 Leibniz’ Calculus: 1673–1675 318
5.13 Leibniz’ Calculus: 1676–1680 329
5.14 The Arithmetical Quadrature 340
5.15 Leibniz’ Publications 349
5.16 The Aftermath 358
6 CONVERGENCE 368
6.1 To the Limit 368
6.2 The Vibrating String Makes Waves 369
6.3 Fourier Puts on the Heat 373
6.4 The Convergence of Series 380
6.5 The Difference Quotient 394
6.6 The Derivative 401
6.7 Cauchy’s Integral Calculus 405
6.8 Uniform Convergence 407
BIBLIOGRAPHY 412

Algebra and Trigonometry

Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger

Addison-Wesley | 2007 | 3ª edição | 1014 páginas | pdf | 22 MB

f3.tiera.ru

lib.freescienceengineering.org

Beecher, Penna, and Bittinger’s Algebra and Trigonometry is known for enabling students to “see the math” through its focus on visualization and early introduction to functions. With the Fourth Edition, the authors continue to innovate by incorporating more ongoing review to help students develop their understanding and study effectively. Mid-chapter Review exercise sets have been added to give students practice in synthesizing the concepts, and new Study Summaries provide built-in tools to help them prepare for tests. The MyMathLab course (access kit required) has been expanded so that the online content is even more integrated with the text’s approach, with the addition of Vocabulary, Synthesis, and Mid-chapter Review exercises from the text as well as example-based videos created by the authors.

The Complete Idiot's Guide to Trigonometry

Izolda Fotiyeva
Dmitriy Fotiyev 


ALPHA | 2012 | 385 páginas | RAR - PDF | 5,12 Mb

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20121013gt

Contents

Part 1: The Basic Tools.. 1
1 What Is Trigonometry?...3

2 Geometry Tools Needed to Study Trigonometry...9
3 Algebra Tools Needed to Study Trigonometry....23

Part 2: Triangle Trigonometry..... 37
4 Trigonometric Functions and Right Triangles..... 39
5 Relations Among Trigonometric Ratios......55
6 The Law of Sines.... 71
7 The Law of Cosines.....85

Part 3: Trigonometric Functions and the Unit Circle...... 101
8 Angles and Rotations....103
9 The Unit Circle Approach...... 121
10 Trigonometric Functions of Any Angle... 133

Part 4: Graphs of Trigonometric Functions.. 145
11 Graphs of Sine and Cosine Functions.... 147
12 Graphs of Other Trigonometric Functions... 163
13 Graphs of Inverse Trigonometric Functions.... 179

Part 5: Trigonometric Identities and Equations...193
14 Kaleidoscope of Identities...195
15 Verifying Trigonometric Identities..205
16 Solving Trigonometric Equations... 217
17 Sum and Difference Formulas... 227

18 Double-Angle and Power-Reducing Formulas... 239
19 Half-Angle and Product-to-Sum Formulas.........249

Part 6: Polar Coordinates and Complex Numbers..........259
20 Polar Coordinates.......261

21 Complex Numbers and Operations with Them.... 275
22 Trigonometry and Calculators......291

Trigonometry

I. M. Gelfand, Mark Saul

Birkhäuser Boston  | 2001 | 239 páginas | PDF | 5,1 Mb

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Trigonometry, a work in the collection of the Gelfand School Program, is the result of a collaboration between two experienced pre-college teachers, one of whom, I.M. Gelfand, is considered to be among our most distinguished living mathematicians. His impact on generations of young people, some now mathematicians of renown, continues to be remarkable. Trigonometry covers all the basics of the subject through beautiful illustrations and examples. The definitions of the trigonometric functions are geometrically motivated. Geometric relationships are rewritten in trigonometric form and extended. The text then makes a transition to the study of algebraic and analytic properties of trigonometric functions, in a way that provides a solid foundation for more advanced mathematical discussions. Throughout, the treatment stimulates the reader to think of mathematics as a unified subject 
Like other I.M. Gelfand treasures in the program—Algebra, Functions and Graphs, and The Method of Coordinates—Trigonometry is written in an engaging style, and approaches the material in a unique fashion that will motivate students and teachers alike. From a review of Algebra, I.M. Gelfand and A. Shen, ISBN 0-8176-3677-3: "The idea behind teaching is to expect students to learn why things are true, rather than have them memorize ways of solving a few problems, as most of our books have done. [This] same philosophy lies behind the current text by Gel'fand and Shen. There are specific 'practical' problems but there is much more development of the ideas.... [The authors] have shown how to write a serious yet lively book on algebra." —R. Askey, The American Mathematics Monthly.

Outros livros de I. M. Gelfand, disponíveis no blog

I.M. Gelfand, Alexander Shen (2003). Algebra. Birkhäuser Boston
Izrailʹ Moiseevich Gelʹ fand, Elena Georgievna Glagoleva, E. E. Shnol (1990). Functions and Graphs. Birkhäuser Boston
I. Gelfand E. Glagolieva A. Kirillow (1990). The Method of Coordinates . Birkhäuser Boston

College Trigonometry

Richard N. Aufmann, Vernon C. Barker, Richard D. Nation

6.ª edição

Books Colee | 2007  | 640 páginas | PDF | 14,8 Mb

link

rapidgator.net

Accessible to students and flexible for instructors, College Trigonometry, Sixth Edition, uses the dynamic link between concepts and applications to bring mathematics to life. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, work independently, and obtain greater mathematical fluency. The text also includes technology features to accommodate courses that allow the option of using graphing calculators. Additional program components that support student success include Eduspace tutorial practice, online homework, SMARTHINKING Live Online Tutoring, and Instructional DVDs.The authors' proven Aufmann Interactive Method allows students to try a skill as it is presented in example form. This interaction between the examples and Try Exercises serves as a checkpoint to students as they read the textbook, do their homework, or study a section. In the Sixth Edition, Review Notes are featured more prominently throughout the text to help students recognize the key prerequisite skills needed to understand new concepts.

Table of contents
1. Functions and Graphs
1.1 Equations and Inequalities
1.2 A Two-Dimensional Coordinate System and Graphs
1.3 Introduction to Functions
1.4 Properties of Graphs
1.5 The Algebra of Functions
1.6 Inverse Functions
1.7 Modeling Data Using Regression
2. Trigonometric Functions
2.1 Angles and Arcs
2.2 Right Angle Trigonometry
2.3 Trigonometric Functions of Any Angle
2.4 Trigonometric Functions of Real Numbers
2.5 Graphs of the Sine and Cosine Functions
2.6 Graphs of the Other Trigonometric Functions
2.7 Graphing Techniques
2.8 Harmonic Motion--An Application of the Sine and Cosine Functions
3. Trigonometric Identities and Equations
3.1 Verification of Trigonometric Identities
3.2 Sum, Difference, and Cofunction Identities
3.3 Double- and Half-Angle Identities
3.4 Identities Involving the Sum of Trigonometric Functions
3.5 Inverse Trigonometric Functions
3.6 Trigonometric Equations
4. Applications of Trigonometry
4.1 The Law of Sines
4.2 The Law of Cosines and Area
4.3 Vectors
5. Complex Numbers
5.1 Complex Numbers
5.2 Trigonometric Form of Complex Numbers
5.3 De Moivre's Theorem
6. Topics in Analytic Geometry
6.1 Parabolas
6.2 Ellipses
6.3 Hyperbolas
6.4 Rotation of Axes
6.5 Introduction to Polar Coordinates
6.6 Polar Equations of the Conics
6.7 Parametric Equations
7. Exponential and Logarithmic Functions
7.1 Exponential Functions and Their Applications
7.2 Logarithmic Functions and Their Applications
7.3 Properties of Logarithms and Logarithmic Scales
7.4 Exponential and Logarithmic Functions
7.5 Exponential Growth and Decay
7.6 Modeling Data with Exponential and Logarithmic Functions

Problems in Geometry

A. Kutepov, A. Rubanov

Mir Publishers, Moscow | 1978| 208 páginas | PDF | 21,1 Mb

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1.ª edição 1975, 2.ª edição 1978.

The book contains a collection of 1351 problems (with answers) in plane and solid geometry for technical schools and colleges. The problems are of varied content, involving calculations, proof, construction of diagrams, and determination of the spatial location of geometrical points. It gives sufficient problems to meet the needs of students for practical work in geometry, and the requirements of the teacher for varied material for tests, etc

Contents

CHAPTER I. REVIEW PROBLEMS

1. The Ratio and Proportionality of Line Segments,
Similarity of Triangles 7
2. Metric Relationships in a Right-Angled Triangle 10
3. Regular Polygons, the Length of the Circumference
and the Arc 15
4. Areas of Plane Figures 17

CHAPTER II. SOLVING TRIANGLES

5. Solving Right-Angled Triangles 22
6. Solving Oblique Triangles 29
Law of Cosines 29
Law of Sines 31
Areas of Triangles, Parallelograms and
Quadrilaterals 32
Basic Cases of Solving Oblique Triangles 34
Particular Cases of Solving Oblique Triangles 34
Heron’s Formula 35
Radii r and R of Inscribed and Circumscribed Circles and the Area S of a Triangle 36
Miscellaneous Problems 37

CHAPTER III. STRAIGHT LINES AND PLANES IN SPACE

7. Basic Concepts and Axioms. Two Straight Lines in Space 43
8. Straight Lines Perpendicular and Inclined to a Plane 46
9. Angles Formed by a Straight Line and a Plane  52
10. Parallelism of a Straight Line and a Plane 55
11. Parallel Planes  59
12. Dihedral Angles. Perpendicular Planes 63
13. Areas of Projections of Plane Figures 67
14 Polyhedral Angles 69

CHAPTER IV. POLYHEDRONS AND ROUND SOLIDS

15. Prisms and Parallelepipeds 71
16. The Pyramid 77
17. The Truncated Pyramid 81
18. Regular Polyhedrons 84
19. The Right Circular Cylinder 86
20. The Right Circular Cone 89
21. The Truncated Cone 93

CHAPTER V. AREAS OF POLYHEDRONS AND ROUND SOLIDS

22. Areas of Parallelepipeds and Prisms 97
23. Areas of Pyramids 102
24. Areas of Truncated Pyramids 105
25. Areas of Cylinders 108
26. Areas of Cones Ill
27. Areas of Truncated Cones 115

CHAPTER VI. VOLUMES OF POLYHEDRONS AND ROUND SOLIDS

28. Volumes of Parallelepipeds 118
29. Volumes of Prisms 122
30. Volumes of Pyramids 127
31. Volumes of Truncated Pyramids 133
32. Volumes of Cylinders 137
33. Volumes of Cones 141
34. Volumes of Truncated Cones 145

CHAPTER VII. THE SPHERE

35. Spheres 149
36. Areas of Spheres and Their Parts 152
37. Volumes of Spheres and Their Parts 155
38. Inscribed and Circumscribed Spheres 159

CHAPTER VIII. APPLYING TRIGONOMETRY TO SOLVING GEOMETRIC PROBLEMS

39. Polyhedrons 164
40. Round Solids 168
41. Areas and Volumes of Prisms 172
42. Areas and Volumes of Pyramids  176
43. Areas and Volumes of Round Solids . 181
Answers 187

A treatise on plane trigonometry

Ernest William Hobson

1918 | Cambridge University Press

online: archive.org

Trigonometry Demystified

Stan Gibilisco

McGraw-Hill Professional | 2003 | 303 páginas | PDF | 5 Mb

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Now anyone with an interest in basic, practical trigonometry can master it -- without formal training, unlimited time, or a genius IQ. In Trigonometry Demystified, best-selling author Stan Gibilisco provides a fun, effective, and totally painless way to learn the fundamentals and general concepts of trigonometry.

With Trigonometry Demystified you master the subject one simple step at a time -- at your own speed. Unlike most books on trigonometry, this book uses prose and illustrations to describe the concepts where others leave you pondering abstract symbology. This unique self-teaching guide offers questions at the end of each chapter and section to pinpoint weaknesses, and a 100-question final exam to reinforce the entire book.

Simple enough for beginners but challenging enough for professional enrichment, Trigonometry Demystified is your direct route to learning or brushing up on trigonometry.

Learn all aspects of trigonometry:
* How angles are expressed
* The relationships between angles and distances
* Calculating distances based on parallax
* Coordinate systems and navigation

Preface
Acknowledgments
PART ONE: WHAT IS TRIGONOMETRY?
Chapter 1. The Circle Model
Chapter 2. A Flurry of Facts
Chapter 3. Graphs and Inverses
Chapter 4. Hyperbolic Functions
Chapter 5. Polar Coordinates
Chapter 6. Three-Space and Vectors
Test: PartOne
PART TWO: HOW IS TRIGONOMETRY USED?
Chapter 7. Scientific Notation
Chapter 8. Surveying, Navigation, and Astronomy
Chapter 9. Waves and Phase
Chapter 10. Reflection and Refraction
Chapter 11. Global Trigonometry
Test: Part Two
FINAL EXAM
ANSWERS TO QUIZ, TEST, AND EXAM QUESTIONS
SUGGESTED ADDITIONAL REFERENCES
INDEX

Teach Yourself Trigonometry

P. Abbott, M.E. Wardle

2.ª edição

Teach Yourself Books | 2003 | PDF | 176 páginas | 45,9 Mb

link

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Teach Yourself Trigonometry, now fully revised and updated to take account of recent trends in mathematics, is suitable for beginners and those needing to brush up their skills. It covers the basics in depth, then goes on to give comprehensive coverage of more advanced trigonometry. Each chapter contains a number of worked examples and many carefully graded exercises. Full demonstrations of trigonometric proofs are given in the answers.

1.ª edição

Ntc Pub Group | 1992 | 193 páginas | PDF | 5 Mb

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scribd.com

Trigonometry Workbook for Dummies

M. Sterling

452 páginas | 2005 | PDF | 3 Mb

link direto

filefactory.com
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From angles to functions to identities - solve trig equations with ease

Got a grasp on the terms and concepts you need to know, but get lost halfway through a problem or worse yet, not know where to begin? No fear - this hands-on-guide focuses on helping you solve the many types of trigonometry equations you encounter in a focused, step-by-step manner. With just enough refresher explanations before each set of problems, you'll sharpen your skills and improve your performance. You'll see how to work with angles, circles, triangles, graphs, functions, the laws of sines and cosines, and more!

100s of Problems!
* Step-by-step answer sets clearly identify where you went wrong (or right) with a problem
* Get the inside scoop on graphing trig functions
* Know where to begin and how to solve the most common equations
* Use trig in practical applications with confidence

Trigonometry

Cynthia Y. Young

3.ª edição

Wiley | 2011 | 746 páginas | PDF | 50 Mb

link

The third edition of Cynthia Young's Trigonometry brings together all the elements that have allowed instructors and learners to successfully "bridge the gap" between classroom instruction and independent homework by overcoming common learning barriers and building confidence in students' ability to do mathematics. Written in a clear, single voice that speaks to students and mirrors how instructors communicate in lecture, Young's hallmark pedagogy enables students to become independent, successful learners. Varied exercise types and modeling projects keep the learning fresh and motivating. Young continues her tradition of fostering a love for succeeding in mathematics by introducing inquiry-based learning projects in this edition, providing learners an opportunity to master the material with more freedom while reinforcing mathematical skills and intuition.

The seamless integration of Cynthia Young's Trigonometry 3^rd editionwith WileyPLUS, a research-based, online environment for effective teaching and learning, continues Young's vision of building student confidence in mathematics because it takes the guesswork out of studying by providing them with a clear roadmap: what to do, how to do it, and whether they did it right.

Conteúdos
1 Right Triangle Trigonometry 2

1.1 Angles, Degrees, and Triangles 4

1.2 Similar Triangles 17

1.3 Definition 1 of Trigonometric Functions: Right Triangle Ratios 28

1.4 Evaluating Trigonometric Functions: Exactly and with Calculators 38

1.5 Solving Right Triangles 49

Inquiry-Based Learning Project 63 | Modeling Our World 65 |

Review 67 | Review Exercises 70 | Practice Test 73

2 Trigonometric Functions 74

2.1 Angles in the Cartesian Plane 76

2.2 Definition 2 of Trigonometric Functions: The Cartesian Plane 84

2.3 Evaluating Trigonometric Functions for Nonacute Angles 93

2.4 Basic Trigonometric Identities 110

Inquiry-Based Learning Project 120 | Modeling Our World 121 |

Review 122 | Review Exercises 124 | Practice Test 126 |

Cumulative Test 127

3 Radian Measure and the Unit Circle Approach 128

3.1 Radian Measure 130

3.2 Arc Length and Area of a Circular Sector 141

3.3 Linear and Angular Speeds 151

3.4 Definition 3 of Trigonometric Functions: Unit Circle Approach 159

Inquiry-Based Learning Project 170 | Modeling Our World 171 |

Review 172 | Review Exercises 174 | Practice Test 176 |

Cumulative Test 177

4 Graphing Trigonometric Functions 178

4.1 Basic Graphs of Sine and Cosine Functions: Amplitude and Period 180

4.2 Translations of the Sine and Cosine Functions: Addition of Ordinates 204

4.3 Graphs of Tangent, Cotangent, Secant, and Cosecant Functions 226

Inquiry-Based Learning Project 246 | Modeling Our World 247 |

Review 248 | Review Exercises 251 | Practice Test 254 |

Cumulative Test 255

5 Trigonometric Identities 256

5.1 Trigonometric Identities 258

5.2 Sum and Difference Identities 268

5.3 Double-Angle Identities 281

5.4 Half-Angle Identities 290

5.5 Product-to-Sum and Sum-to-Product Identities 300

Inquiry-Based Learning Project 309 | Modeling Our World 310 |

Review 311 | Review Exercises 313 | Practice Test 316 |

Cumulative Test 317

6 Solving Trigonometric Equations 318

6.1 Inverse Trigonometric Functions 320

6.2 Solving Trigonometric Equations That Involve Only One Trigonometric Function 342

6.3 Solving Trigonometric Equations That Involve Multiple Trigonometric Functions 353

Inquiry-Based Learning Project 360 | Modeling Our World 362 |

Review 363 | Review Exercises 366 | Practice Test 368 |

Cumulative Test 369

7 Applications of Trigonometry: Triangles and Vectors 370

7.1 Oblique Triangles and the Law of Sines 372

7.2 The Law of Cosines 387

7.3 The Area of a Triangle 397

7.4 Vectors 405

7.5 The Dot Product 421

Inquiry-Based Learning Project 429 | Modeling Our World 430 |

Review 431 | Review Exercises 433 | Practice Test 436 |

Cumulative Test 437

8 Complex Numbers, Polar Coordinates, and Parametric Equations 438

8.1 Complex Numbers 440

8.2 Polar (Trigonometric) Form of Complex Numbers 447

8.3 Products, Quotients, Powers, and Roots of Complex Numbers: De Moivre’s Theorem 456

8.4 Polar Equations and Graphs 469

8.5 Parametric Equations and Graphs 483

Inquiry-Based Learning Project 494 | Modeling Our World 495 |

Review 497 | Review Exercises 499 | Practice Test 501 |

Cumulative Test 502

Appendix A Algebraic Prerequisites and Review 503

A.1 Factoring Polynomials 504

A.2 Basic Tools: Cartesian Plane, Distance, and Midpoint 515

A.3 Graphing Equations: Point-Plotting, Intercepts, and Symmetry 523

A.4 Functions 535

A.5 Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change 554

A.6 Graphing Techniques: Transformations 574

A.7 Operations on Functions and Composition of Functions 589

A.8 One-to-One Functions and Inverse Functions 599

Review 614 | Review Exercises 617 | Practice Test 621

Appendix B Conic Sections 623

B.1 Conic Basics 624

B.2 The Parabola 627

B.3 The Ellipse 640

B.4 The Hyperbola 652

B.5 Rotation of Axes 664

B.6 Polar Equations of Conics 674

Review 685 | Review Exercises 688 | Practice Test 691

Answers to Odd Numbered Exercises 692

Applications Index 738

Subject Index 740