Trigonometry For Dummies

**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 5 Table of Contents 7 Introduction 15 About This Book 15 Foolish Assumptions 16 Icons Used in This Book 17 Beyond the Book 17 Where to Go from Here 18 Part I: Getting Started with Trigonometry 19 Chapter 1: Trouncing Trig Technicalities. 21 Taking Trig for a Ride: What Trig Is 21 Understanding Trig Speak 32 Equating and Identifying 37 Graphing for Gold 39 Chapter 2: Coordinating Your Efforts with Cartesian Coordinates. 43 Starting Out Simple: Plotting Points 43 From Here to There: Calculating Distances 46 Getting to the Center of It All 50 Racing Down the Slope 57 Defining Circles with Numbers 59 Chapter 3: Functioning Well. 61 Relations versus Functions 61 In-Verse Functions: Rhyme or Reason? 64 Transforming Functions 68 Chapter 4: Getting Your Degree. 71 Angles, Angles Everywhere: Measuring in Degrees 71 Graphing Angles in Standard Position 76 What’s Your Angle? Labeling in Various Ways 78 Chapter 5: Dishing Out the Pi: Radians. 81 What’s in a Radian? 81 Making a Clone of Arc 87 Chapter 6: Getting It Right with Triangles. 95 Sizing Up Right Triangles 95 Pythagoras Schmythagoras: Demystifying the Pythagorean Theorem 98 In a League of Their Own: Special Right Triangles 102 Part II: Trigonometric Functions 105 Chapter 7: Doing Right by Trig Functions. 107 SohCahToa to the Rescue: How Trig Functions Work 107 Taking It a Step Further: Reciprocal Functions 115 Angling In on Your Favorites 118 Chapter 8: Trading Triangles for Circles: Circular Functions. 123 Getting Acquainted with the Unit Circle 123 Going Full Circle with the Angles 130 Chapter 9: Defining Trig Functions Globally. 135 Defining Trig Functions for All Angles 135 Using Coordinates of Circles to Solve for Trig Functions 139 Defining Domains and Ranges of Trig Functions 144 Chapter 10: Applying Yourself to Trig Functions. 149 First Things First: Elevating and Depressing 149 Measuring Tall Buildings with a Single Bound 151 Measuring Slope 156 The Sky’s (Not) the Limit 157 Calculating Odd Shapes and Maneuvering Corners 163 Part III: Identities 169 Chapter 11: Identifying Basic Identities. 171 Flipping Functions on Their Backs: Reciprocal Identities 171 Function to Function: Ratio Identities 173 Opposites Attract: Opposite-Angle Identities 173 Revisiting the Classic Theorem: Pythagorean Identities 176 Combining the Identities 182 Chapter 12: Operating on Identities. 185 Summing It Up 185 Overcoming the Differences 190 Doubling Your Money 193 Halving Fun Yet? 198 Chapter 13: Proving Identities: The Basics. 203 Lining Up the Players 203 Picking Sides 205 Working on Both Sides 209 Going Back to Square One 212 Chapter 14: Sleuthing Out Identity Solutions. 221 Fracturing Fractions 221 Using Tricks of the Trig Trade 226 Identifying With the Operations 230 Part IV: Equations and Applications 237 Chapter 15: Investigating Inverse Trig Functions. 239 Writing It Right 239 Determining Domain and Range of Inverse Trig Functions 243 Chapter 16: Making Inverse Trig Work for You. 247 Working with Inverses 247 Getting Friendly with Your Calculator 249 Multiplying the Input 252 Solving Some Mixed Problems 254 Chapter 17: Solving Trig Equations. 257 Generating Simple Solutions 258 Factoring In the Solutions 259 Using the Quadratic Formula 267 Incorporating Identities 268 Finding Multiple-Angle Solutions 272 Squaring Both Sides 273 Multiplying Through 276 Solving with a Graphing Calculator 276 Chapter 18: Obeying the Laws. 279 Describing the Parts of Triangles 279 Following the Law of Sines 282 Continuing with the Law of Cosines 286 Finding the Areas of Triangles 295 Part V: The Graphs of Trig Functions 303 Chapter 19: Graphing Sine and Cosine. 305 The ABCs of Graphing 305 Waving at the Sine 306 Graphing Cosine 312 Applying the Sines of the Times 314 Chapter 20: Graphing Tangent and Cotangent. 321 Checking Out Tangent 321 Confronting the Cotangent 328 Chapter 21: Graphing Other Trig Functions. 331 Seeing the Cosecant for What It Is 331 Unveiling the Secant 335 Laying Out the Inverse Functions 338 Chapter 22: Topping Off Trig Graphs. 343 The Basics of Trig Equations 343 Graphing with the General Form 346 Adding and Subtracting Functions 351 Applying Yourself to the Task 353 Part VI: The Part of Tens 357 Chapter 23: Ten Basic Identities 359 Reciprocal Identities 359 Ratio Identities 360 Pythagorean Identities 361 Opposite-Angle Identities 361 Multiple-Angle Identities 362 Chapter 24: Ten Not-So-Basic Identities. 363 Product-to-Sum Identities 363 Sum-to-Product Identities 364 Reduction Formula 365 Mollweide’s Equations 366 Appendix: Trig Functions Table 367 Index 371 About the Author 383 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. 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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.