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| Introduction | |
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| About This Book | |
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| Conventions Used in This Book | |
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| Foolish Assumptions | |
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| How This Book Is Organized | |
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| Icons Used in This Book | |
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| Where to Go from Here | |
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| Trying Out Trig: Starting at the Beginning | |
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| Tackling Technical Trig | |
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| Getting Angles Labeled by Size | |
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| Naming Angles Where Lines Intersect | |
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| Writing Angle Names Correctly | |
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| Finding Missing Angle Measures in Triangles | |
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| Determining Angle Measures along Lines and outside Triangles | |
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| Dealing with Circle Measurements | |
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| Tuning In with the Right Chord | |
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| Sectioning Off Sectors of Circles | |
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| Answers to Problems on Tackling Technical Trig | |
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| Getting Acquainted with the Graph | |
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| Plotting Points | |
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| Identifying Points by Quadrant | |
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| Working with Pythagoras | |
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| Keeping Your Distance | |
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| Finding Midpoints of Segments | |
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| Dealing with Slippery Slopes | |
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| Writing Equations of Circles | |
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| Graphing Circles | |
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| Answers to Problems on Graphing | |
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| Getting the Third Degree | |
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| Recognizing First-Quadrant Angles | |
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| Expanding Angles to Other Quadrants | |
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| Expanding Angles beyond 360 Degrees | |
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| Coordinating with Negative Angle Measures | |
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| Dealing with Coterminal Angles | |
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| Answers to Problems on Measuring in Degrees | |
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| Recognizing Radian Measure | |
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| Becoming Acquainted with Graphed Radians | |
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| Changing from Degrees to Radians | |
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| Changing from Radians to Degrees | |
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| Measuring Arcs | |
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| Determining the Area of a Sector | |
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| Answers to Problems on Radian Measure | |
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| Making Things Right with Right Triangles | |
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| Naming the Parts of a Right Triangle | |
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| Completing Pythagorean Triples | |
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| Completing Right Triangles | |
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| Working with the 30-60-90 Right Triangle | |
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| Using the Isosceles Right Triangle | |
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| Using Right Triangles in Applications | |
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| Answers to Problems on Right Triangles | |
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| Trigonometric Functions | |
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| Defining Trig Functions with a Right Triangle | |
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| Defining the Sine Function | |
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| Cooperating with the Cosine Function | |
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| Sunning with the Tangent Definition | |
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| Hunting for the Cosecant Definition | |
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| Defining the Secant Function | |
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| Coasting Home with the Cotangent | |
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| Establishing Trig Functions for Angles in Special Right Triangles | |
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| Applying the Trig Functions | |
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| Answers to Problems on Defining Trig Functions | |
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| Discussing Properties of the Trig Functions | |
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| Defining a Function an Its Inverse | |
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| Deciding on the Domains | |
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| Reaching Out for the Ranges | |
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| Closing In on Exact Values | |
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| Determining Exact Values for All Functions | |
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| Answers to Problems in Properties of Trig Functions | |
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| Going Full Circle with the Circular Functions | |
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| Finding Points on the Unit Circle | |
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| Determining Reference Angles | |
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| Assigning the Signs of Functions by Quadrant | |
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| Figuring Out Trig Functions around the Clock | |
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| Answers to Problems in Going Full Circle | |
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| Trigonometric Identities and Equations | |
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| Identifying the Basic Identities | |
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| Using the Reciprocal Identities | |
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| Creating the Ratio Identities | |
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| Playing Around with Pythagorean Identities | |
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| Solving Identities Using Reciprocals, Ratios, and Pythagoras | |
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| Answers to Problems on Basic Identities | |
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| Using Identities Defined with Operations | |
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| Adding Up the Angles with Sum Identities | |
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| Subtracting Angles with Difference Identities | |
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| Doubling Your Pleasure with Double Angle Identities | |
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| Multiplying the Many by Combining Sums and Doubles | |
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| Halving Fun with Half-Angle Identities | |
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| Simplifying Expressions with Identities | |
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| Solving Identities | |
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| Answers to Problems on Using Identities | |
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| Techniques for Solving Trig Identities | |
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| Working on One Side at a Time | |
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| Working Back and Forth on Identities | |
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| Changing Everything to Sine and Cosine | |
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| Multiplying by Conjugates | |
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| Squaring Both Sides | |
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| Finding Common Denominators | |
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| Writing All Functions in Terms of Just One | |
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| Answers to Problems Techniques for Solving Identities | |
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| Introducing Inverse Trig Functions | |
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| Determining the Correct Quadrants | |
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| Evaluating Expressions Using Inverse Trig Functions | |
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| Solving Equations Using Inverse Trig Functions | |
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| Creating Multiple Answers for Multiple and Half-Angles | |
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| Answers to Problems on Inverse Trig Functions | |
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| Solving Trig Equations | |
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| Solving for Solutions within One Rotation | |
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| Solving Equations with Multiple Answers | |
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| Special Factoring for a Solution | |
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| Using Fractions and Common Denominators to Solve Equations | |
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| Using the Quadratic Formula | |
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| Answers to Problems on Solving Trig Equations | |
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| Revisiting the Triangle with New Laws | |
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| Using the Law of Sines | |
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| Adding the Law of Cosines | |
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| Dealing with the Ambiguous Case | |
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| Investigating the Law of Tangents | |
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| Finding the Area of a Triangle the Traditional Way | |
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| Flying In with Heron's Formula | |
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| Finding Area with an Angle Measure | |
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| Applying Triangles | |
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| Answers to Problems on Triangles | |
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| Graphing the Trigonometric Functions | |
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| Graphing Sine and Cosine | |
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| Determining Intercepts and Extreme Values | |
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| Graphing the Basic Sine and Cosine Curves | |
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| Changing the Amplitude | |
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| Adjusting the Period of the Curves | |
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| Graphing from the Standard Equation | |
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| Applying the Sine and Cosine Curves to Life | |
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| Answers to Problems on Graphing Sine and Cosine | |
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| Graphing Tangent and Cotangent | |
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| Establishing Vertical Asymptotes | |
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| Graphing Tangent and Cotangent | |
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| Altering the Basic Curves | |
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| Answers to Problems on Graphing Tangent and Cotangent | |
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| Graphing Cosecant, Secant, and Inverse Trig Functions | |
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| Determining the Vertical Asymptotes | |
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| Graphing Cosecant and Secant | |
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| Making Changes to the Graphs of Cosecant and Secant | |
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| Analyzing the Graphs of the Inverse Trig Functions | |
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| Answers to Problems on Cosecant, Secant, and Inverse Trig Functions | |
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| Transforming Graphs of Trig Functions | |
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| Sliding the Graphs Left or Right | |
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| Sliding the Graphs Up or Down | |
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| Changing the Steepness | |
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| Reflecting on the Situation - Horizontally | |
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| Reflecting on Your Position - Vertically | |
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| Putting It All Together | |
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| Combining Trig Functions with Polynomials | |
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| Answers to Problems on Transforming Trig Functions | |
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| The Part of Tens | |
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| Ten Identities with a Negative Attitude | |
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| Negative Angle Identities | |
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| Complementing and Supplementing Identities | |
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| Doing Fancy Factoring with Identities | |
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| Ten Formulas to Use in a Circle | |
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| Running Around in Circles | |
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| Adding Up the Area | |
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| Defeating an Arc Rival | |
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| Sectioning Off the Sector | |
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| Striking a Chord | |
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| Ringing True | |
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| Inscribing and Radii | |
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| Circumscribing and Radii | |
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| Righting a Triangle | |
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| Inscribing a Polygon | |
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| Ten Ways to Relate the Sides and Angles of Any Triangle | |
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| Relating with the Law of Sines | |
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| Hatching a Little Heron | |
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| Summing Sines | |
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| You Half It or You Don't | |
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| Cozying Up with Cosines | |
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| Angling for an Angle | |
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| Mixing It Up with Cosines | |
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| Heron Again, Gone Tomorrow | |
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| Divide and Conquer with the Tangent | |
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| Heron Lies the Problem | |
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| Trig Functions Table | |
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| Index | |