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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 | |