Trigonometry Workbook For Dummies

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ISBN: 9780764587818 | 0764587811
Cover: Paperback
Copyright: 7/8/2005

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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

Introduction

(1)

About This Book

(1)

Conventions Used in This Book

(1)

Foolish Assumptions

(1)

How This Book Is Organized

(2)

Part I: Trying Out Trig: Starting at the Beginning

(1)

Part II: Trigonometric Functions

(1)

Part III: Trigonometric Identities and Equations

(1)

Part IV: Graphing the Trigonometric Functions

(1)

Part V: The Part of Tens

(1)

Icons Used in This Book

(1)

Where to Go from Here

(1)

Part I: Trying Out Trig: Starting at the Beginning

(70)

Tackling Technical Trig

(14)

Getting Angles Labeled by Size

(2)

Naming Angles Where Lines Intersect

(1)

Writing Angle Names Correctly

(1)

Finding Missing Angle Measures in Triangles

(1)

Determining Angle Measures along Lines and outside Triangles

(2)

Dealing with Circle Measurements

(1)

Tuning In with the Right Chord

(1)

Sectioning Off Sectors of Circles

(1)

Answers to Problems on Tackling Technical Trig

(4)

Getting Acquainted with the Graph

(16)

Plotting Points

(2)

Identifying Points by Quadrant

(1)

Working with Pythagoras

(2)

Keeping Your Distance

(1)

Finding Midpoints of Segments

(1)

Dealing with Slippery Slopes

(2)

Writing Equations of Circles

(2)

Graphing Circles

(1)

Answers to Problems on Graphing

(4)

Getting the Third Degree

(8)

Recognizing First-Quadrant Angles

(2)

Expanding Angles to Other Quadrants

(1)

Expanding Angles beyond 360 Degrees

(1)

Coordinating with Negative Angle Measures

(1)

Dealing with Coterminal Angles

(1)

Answers to Problems on Measuring in Degrees

(2)

Recognizing Radian Measure

(12)

Becoming Acquainted with Graphed Radians

(2)

Changing from Degrees to Radians

(2)

Changing from Radians to Degrees

(1)

Measuring Arcs

(2)

Determining the Area of a Sector

(1)

Answers to Problems on Radian Measure

(4)

Making Things Right with Right Triangles

(18)

Naming the Parts of a Right Triangle

(2)

Completing Pythagorean Triples

(2)

Completing Right Triangles

(1)

Working with the 30-60-90 Right Triangle

(2)

Using the Isosceles Right Triangle

(1)

Using Right Triangles in Applications

(3)

Answers to Problems on Right Triangles

(7)

Part II: Trigonometric Functions

(44)

Defining Trig Functions with a Right Triangle

(16)

Defining the Sine Function

(1)

Cooperating with the Cosine Function

(1)

Sunning with the Tangent Definition

(1)

Hunting for the Cosecant Definition

(1)

Defining the Secant Function

(1)

Coasting Home with the Cotangent

(2)

Establishing Trig Functions for Angles in Special Right Triangles

(1)

Applying the Trig Functions

(2)

Answers to Problems on Defining Trig Functions

(5)

Discussing Properties of the Trig Functions

(12)

Defining a Function and Its Inverse

(2)

Deciding on the Domains

(2)

Reaching Out for the Ranges

(1)

Closing In on Exact Values

(1)

Determining Exact Values for All Functions

(3)

Answers to Problems in Properties of Trig Functions

102

(3)

Going Full Circle with the Circular Functions

105

(14)

Finding Points on the Unit Circle

105

(3)

Determining Reference Angles

108

(3)

Assigning the Signs of Functions by Quadrant

111

(2)

Figuring Out Trig Functions around the Clock

113

(2)

Answers to Problems in Going Full Circle

115

(4)

Part III: Trigonometric Identities and Equations

119

(112)

Identifying the Basic Identities

121

(14)

Using the Reciprocal Identities

121

(2)

Creating the Ratio Identities

123

(1)

Playing Around with Pythagorean Identities

124

(3)

Solving Identities Using Reciprocals, Ratios, and Pythagoras

127

(3)

Answers to Problems on Basic Identities

130

(5)

Using Identities Defined with Operations

135

(26)

Adding Up the Angles with Sum Identities

135

(3)

Subtracting Angles with Difference Identities

138

(2)

Doubling Your Pleasure with Double Angle Identities

140

(2)

Multiplying the Many by Combining Sums and Doubles

142

(2)

Halving Fun with Half-Angle Identities

144

(2)

Simplifying Expressions with Identities

146

(2)

Solving Identities

148

(3)

Answers to Problems on Using Identities

151

(10)

Techniques for Solving Trig Identities

161

(24)

Working on One Side at a Time

161

(3)

Working Back and Forth on Identities

164

(1)

Changing Everything to Sine and Cosine

165

(2)

Multiplying by Conjugates

167

(1)

Squaring Both Sides

168

(1)

Finding Common Denominators

169

(2)

Writing All Functions in Terms of Just One

171

(2)

Answers to Problems Techniques for Solving Identities

173

(12)

Introducing Inverse Trig Functions

185

(10)

Determining the Correct Quadrants

185

(2)

Evaluating Expressions Using Inverse Trig Functions

187

(2)

Solving Equations Using Inverse Trig Functions

189

(2)

Creating Multiple Answers for Multiple and Half-Angles

191

(2)

Answers to Problems on Inverse Trig Functions

193

(2)

Solving Trig Equations

195

(18)

Solving for Solutions within One Rotation

195

(2)

Solving Equations with Multiple Answers

197

(3)

Special Factoring for a Solution

200

(2)

Using Fractions and Common Denominators to Solve Equations

202

(3)

Using the Quadratic Formula

205

(1)

Answers to Problems on Solving Trig Equations

206

(7)

Revisiting the Triangle with New Laws

213

(18)

Using the Law of Sines

213

(2)

Adding the Law of Cosines

215

(3)

Dealing with the Ambiguous Case

218

(1)

Investigating the Law of Tangents

219

(1)

Finding the Area of a Triangle the Traditional Way

220

(1)

Flying In with Heron's Formula

221

(1)

Finding Area with an Angle Measure

222

(1)

Applying Triangles

223

(1)

Answers to Problems on Triangles

224

(7)

Part IV: Graphing the Trigonometric Functions

231

(46)

Graphing Sine and Cosine

233

(16)

Determining Intercepts and Extreme Values

233

(2)

Graphing the Basic Sine and Cosine Curves

235

(1)

Changing the Amplitude

236

(2)

Adjusting the Period of the Curves

238

(1)

Graphing from the Standard Equation

239

(2)

Applying the Sine and Cosine Curves to Life

241

(2)

Answers to Problems on Graphing Sine and Cosine

243

(6)

Graphing Tangent and Cotangent

249

(6)

Establishing Vertical Asymptotes

249

(1)

Graphing Tangent and Cotangent

250

(2)

Altering the Basic Curves

252

(1)

Answers to Problems on Graphing Tangent and Cotangent

253

(2)

Graphing Cosecant, Secant, and Inverse Trig Functions

255

(8)

Determining the Vertical Asymptotes

255

(1)

Graphing Cosecant and Secant

256

(1)

Making Changes to the Graphs of Cosecant and Secant

257

(1)

Analyzing the Graphs of the Inverse Trig Functions

258

(3)

Answers to Problems on Cosecant, Secant, and Inverse Trig Functions

261

(2)

Transforming Graphs of Trig Functions

263

(14)

Sliding the Graphs Left or Right

263

(1)

Sliding the Graphs Up or Down

264

(2)

Changing the Steepness

266

(1)

Reflecting on the Situation --- Horizontally

267

(1)

Reflecting on Your Position --- Vertically

268

(1)

Putting It All Together

269

(1)

Combining Trig Functions with Polynomials

270

(2)

Answers to Problems on Transforming Trig Functions

272

(5)

Part V: The Part of Tens

277

(12)

Ten Identities with a Negative Attitude

279

(2)

Negative Angle Identities

279

(1)

Complementing and Supplementing Identities

279

(1)

Doing Fancy Factoring with Identities

280

(1)

Ten Formulas to Use in a Circle

281

(4)

Running Around in Circles

281

(1)

Adding Up the Area

281

(1)

Defeating an Arc Rival

281

(1)

Sectioning Off the Sector

282

(1)

Striking a Chord

282

(1)

Ringing True

283

(1)

Inscribing and Radii

283

(1)

Circumscribing and Radii

283

(1)

Righting a Triangle

284

(1)

Inscribing a Polygon

284

(1)

Ten Ways to Relate the Sides and Angles of Any Triangle

285

(4)

Relating with the Law of Sines

285

(1)

Hatching a Little Heron

286

(1)

Summing Sines

286

(1)

You Half It or You Don't

286

(1)

Cozying Up with Cosines

286

(1)

Angling for an Angle

286

(1)

Mixing It Up with Cosines

286

(1)

Heron Again, Gone Tomorrow

287

(1)

Divide and Conquer with the Tangent

287

(1)

Heron Lies the Problem

287

(2)

Appendix: Trig Functions Table

289

(4)

Index

293

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Trigonometry Workbook For Dummies

Summary

Author Biography

Table of Contents

Supplemental Materials