Trigonometry Books

Book SynopsisAn interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentiethThe Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s. Glen Van Brummelen tells the story of trigonometry as it evolved from an instrument for understanding the heavens to a practical tool, used in fields such as surveying and navigation. In Europe, China, and America, trigonometry aided and was itself transformed by concurrent mathematical revolutions, as well as the rise of science and technology. Following its uses in mid-sixteenth-century Europe as the foot of the ladder to the stars and the mathematical helpmate of astronomy, trigonometry became a ubiquitous tool for modeling various phenomena, including animal populations and sound waves. In the late sixteenth century, trigonometry increasingly entered the physical world through the practical disciplines, and its societal reach expanded

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Book SynopsisMarge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan. When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but afTable of ContentsR. Review of Basic Concepts R.1. Fractions, Decimals, and Percents R.2. Sets and Real Numbers R.3. Real Number Operations and Properties R.4. Integer and Rational Exponents R.5. Polynomials R.6. Factoring Polynomials R.7. Rational Expressions R.8. Radical Expressions 1. Equations and Inequalities 1.1. Linear Equations 1.2. Applications and Modeling with Linear Equations 1.3. Complex Numbers 1.4. Quadratic Equations 1.5. Applications and Modeling with Quadratic Equations 1.6. Other Types of Equations and Applications 1.7. Inequalities 1.8. Absolute Value Equations and Inequalities 2. Graphs and Functions 2.1. Rectangular Coordinates and Graphs 2.2. Circles 2.3. Functions 2.4. Linear Functions 2.5. Equations of Lines and Linear Models 2.6. Graphs of Basic Functions 2.7. Graphing Techniques 2.8. Function Operations and Composition 3. Polynomial and Rational Functions 3.1. Quadratic Functions and Models 3.2. Synthetic Division 3.3. Zeros of Polynomial Functions 3.4. Polynomial Functions: Graphs, Applications, and Models 3.5. Rational Functions: Graphs, Applications, and Models 3.6. Polynomial and Rational Inequalities 3.7. Variation 4. Inverse, Exponential, and Logarithmic Functions 4.1. Inverse Functions 4.2. Exponential Functions 4.3. Logarithmic Functions 4.4. Evaluating Logarithms and the Change-of-Base Theorem 4.5. Exponential and Logarithmic Equations 4.6. Applications of Models of Exponential Growth and Decay 5. Trigonometric Functions 5.1. Angles 5.2. Trigonometric Functions 5.3. Trigonometric Function Values and Angle Measures 5.4. Solutions and Applications of Right Triangles 6. The Circular Functions and Their Graphs 6.1. Radian Measure 6.2. The Unit Circle and Circular Functions 6.3. Graphs of the Sine and Cosine Functions 6.4. Translations of the Graphs of the Sine and Cosine Functions 6.5. Graphs of the Tangent and Cotangent Functions 6.6. Graphs of the Secant and Cosecant Functions 6.7. Harmonic Motion 7. Trigonometric Identities and Equations 7.1. Fundamental Identities 7.2. Verifying Trigonometric Identities 7.3. Sum and Difference Identities 7.4. Double-Angle and Half-Angle Identities 7.5. Inverse Circular Functions 7.6. Trigonometric Equations 7.7. Equations Involving Inverse Trigonometric Functions 8. Applications of Trigonometry 8.1. The Law of Sines 8.2. The Law of Cosines 8.3. Geometrically Defined Vectors and Applications 8.4. Algebraically Defined Vectors and the Dot Product 8.5. Trigonometric (Polar) Form of Complex Numbers; Products and Quotients 8.6. De Moivre's Theorem; Powers and Roots of Complex Numbers 8.7. Polar Equations and Graphs 8.8. Parametric Equations, Graphs, and Applications 9. Systems and Matrices 9.1. Systems of Linear Equations 9.2. Matrix Solution of Linear Systems 9.3. Determinant Solution of Linear Systems 9.4. Partial Fractions 9.5. Nonlinear Systems of Equations 9.6. Systems of Inequalities and Linear Programming 9.7. Properties of Matrices 9.8. Matrix Inverses 10. Analytic Geometry 10.1. Parabolas 10.2. Ellipses 10.3. Hyperbolas 10.4. Summary of the Conic Sections 11. Further Topics in Algebra 11.1. Sequences and Series 11.2. Arithmetic Sequences and Series 11.3. Geometric Sequences and Series 11.4. The Binomial Theorem 11.5. Mathematical Induction 11.6. Basics of Probability Appendix A Polar Form of Conic Sections Appendix B Rotation of Axes Appendix C Geometry Formulas

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Book SynopsisTrigonometry has always been an underappreciated branch of mathematics. It has a reputation as a dry and difficult subject, a glorified form of geometry complicated by tedious computation. In this book, Eli Maor draws on his remarkable talents as a guide to the world of numbers to dispel that view. Rejecting the usual arid descriptions of sine, cosTrade Review"Maor's presentation of the historical development of the concepts and results deepens one's appreciation of them, and his discussion of the personalities involved and their politics and religions puts a human face on the subject. His exposition of mathematical arguments is thorough and remarkably easy to understand. There is a lot of material here that teachers can use to keep their students awake and interested. In short, Trigonometric Delights should be required reading for everyone who teaches trigonometry and can be highly recommended for anyone who uses it."--George H. Swift, American Mathematics Monthly "[Maor] writes enthusiastically and engagingly... Delightful reading from cover to cover. Trigonometric Delights is a welcome addition."--Sean Bradley, MAA Online "Maor clearly has a great love of trigonometry, formulas and all, and his enthusiasm shines through... If you always wanted to know where trigonometry came from, and what it's good for, you'll find plenty here to enlighten you."--Ian Stewart, New Scientist "This book will appeal to a general audience interested in the history of mathematics. I highly recommend [it] to teachers who would like to ground their lessons in the sort of mathematical investigations that were undertaken throughout history."--Richard S. Kitchen, Mathematics TeacherTable of ContentsPreface xi Prologue: Ahmes the Scribe, 1650 B.C. 3 Recreational Mathematics in Ancient Egypt 11 1.Angles 15 2.Chords 20 Plimpton 322: The Earliest Trigonometric Table? 30 3.Six Functions Come of Age 35 Johann Muller, alias Regiomontanus 41 4.Trigonometry Becomes Analytic 50 Francois Viete 56 5.Measuring Heaven and Earth 63 Abraham De Moivre 80 6.Two Theorems from Geometry 87 7.Epicycloids and Hypocycloids 95 Maria Agnesi and Her "Witch" 108 8.Variations on a Theme by Gauss 112 9.Had Zeno Only Known This! 117 10.(sin x)/x 129 11.A Remarkable Formula 139 Jules Lissajous and His Figures 145 12.tan x 150 13.A Mapmaker's Paradise 165 14.sin x = 2: Imaginary Trigonometry 181 Edmund Landau: The Master Rigorist 192 15. Fourier's Theorem 198 Appendixes 211 1.Let's Revive an Old Idea 213 2.Barrow's Integration of sec o 218 3.Some Trigonometric Gems 220 4.Some Special Values of sin alpha 222 Bibliography 225 Credits for Illustrations 229 Index 231

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Book SynopsisTrigonometry is a branch of mathematics that studies relationships between angles and sides of triangles. It involves sine, cosine, and tangent concepts, which calculate angles and sides in various scenarios. Trigonometry has applications in fields such as physics, engineering, and architecture, where understanding the relationships between angles and sides is important. It is a fundamental topic in mathematics and is often studied in high school and college. Overall, trigonometry is crucial in solving problems involving triangles and is used extensively in practical applications. This book Trigonometry Basics: Solving Triangles and Trigonometric Functions is divided in to 8 chapters each delving into specific aspects of this mathematical discipline, from foundational concepts to advanced applications.Table of Contents Chapter 1 Introduction to Trigonometry Chapter 2 The Tangent Chapter 3 Sine and Cosine Chapter 4 Identities and FormulasChapter 5 Triangles Chapter 6 3D Trigonometry and Angles Chapter 7 Trigonometric Functions and Graphs Chapter 8 Trigonometry and Technology

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Book SynopsisTable of ContentsEvery chapter ends with Review Exercises, Discussion Exercises, and a Chapter Test. 1. FUNDAMENTAL CONCEPTS OF ALGEBRA. Real Numbers. Exponents and Radicals. Algebraic Expressions. Fractional Expressions. 2. EQUATIONS AND INEQUALITIES. Equations. Applied Problems. Quadratic Equations. Complex Numbers. Other Types of Equations. Inequalities. More on Inequalities. 3. FUNCTIONS AND GRAPHS. Rectangular Coordinate Systems. Graphs of Equations. Lines. Definition of Function. Graphs of Functions. Quadratic Functions. Operations on Functions. 4. POLYNOMIAL AND RATIONAL FUNCTIONS. Polynomial Functions of Degree Greater than 2. Properties of Division. Zeros of Polynomials. Complex and Rational Zeros of Polynomials. Rational Functions. Variation. 5. INVERSE, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS. Inverse Functions. Exponential Functions. The Natural Exponential Function. Logarithmic Functions. Properties of Logarithms. Exponential and Logarithmic Equations. 6. THE TRIGONOMETRIC FUNCTIONS. Angles. Trigonometric Functions of Angles. Trigonometric Functions of Real Numbers. Values of Trigonometric Functions. Trigonometric Graphs. Additional Trigonometric Graphs. Applied Problems. 7. ANALYTIC TRIGONOMETRY. Verifying Trigonometric Identities. Trigonometric Equations. The Addition and Subtraction Formulas. Multiple-Angle Formulas. Product-to-Sum and Sum-to-Product Formulas. The Inverse Trigonometric Functions. 8. APPLICATIONS OF TRIGONOMETRY. The Law of Sines. The Law of Cosines. Vectors. The Dot Product. Trigonometric Form for Complex Numbers. De Moivre's Theorem and nth Roots of Complex Numbers. 9. SYSTEMS OF EQUATIONS AND INEQUALITIES. Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Inequalities. Linear Programming. Systems of Linear Equations in More than Two Variables. The Algebra of Matrices. The Inverse of a Matrix. Determinants. Properties of Determinants. Partial Fractions. 10. SEQUENCES, SERIES AND PROBABILITY. Infinite Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Mathematical Induction. The Binomial Theorem. Permutations. Distinguishable Permutations and Combinations. Probability. 11. TOPICS FROM ANALYTIC GEOMETRY. Parabolas. Ellipses. Hyperbolas. Plane Curves and Parametric Equations. Polar Coordinates. Polar Equations of Conics. Appendix I: Common Graphs and Their Equations. Appendix II: A Summary of Graph Transformations. Appendix III: Graphs of the Trigonometric Functions and Their Inverses. Appendix IV: Values of the Trigonometric Functions of Special Angles on a Unit Circle.

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Book SynopsisTable of Contents1 Right Triangle Trigonometry 1 2 Trigonometric Functions 68 3 Radian Measure and the Unit Circle Approach 118 4 Graphing Trigonometric Functions 165 5 Trigonometric Identities 237 6 Solving Trigonometric Equations 293 7 Applications of Trigonometry: Triangles and Vectors 341 8 Complex Numbers, Polar Coordinates, and Parametric Equations 405 Appendix A 467 Appendix B 585 Appendix C 654 Answers To Odd-Numbered Exercises 658 Application Index 692 Subject Index 695

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Book SynopsisStrengthen your trigonometry skills and grades with this powerful and simple tool for reviewing and referencing the most important core concepts. Quickly find that answer you need in 6 laminated pages rather than flipping through a large book. Used in the fields of engineering, medical imaging, geography, land surveying, and video game development, to name a few, you may find that trigonometry is here to stay in your career life. Keep this tool by your side and through it all for that extra memory jolt when you need it. Suggested uses: Quick Reference -- instead of digging into a large book to find a core answer you need while studying, use the guide to reinforce quickly and repeatedly; Memory -- refreshing your memory repeatedly is a foundation of studying, have the core labs handy so you can focus on the larger picture.

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