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Preface | |

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Supplements Guide | |

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Trigonometric Functions | |

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Angles | |

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Basic Terminology | |

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Degree Measure | |

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Standard Position | |

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Coterminal Angles | |

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Angle Relationships and Similar Triangles | |

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Geometric Properties | |

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Triangles | |

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Trigonometric Functions | |

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Trigonometric Functions | |

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Quadrantal Angles | |

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Using the Definitions of the Trigonometric Functions | |

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Reciprocal Identities | |

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Signs and Ranges of Function Values | |

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Pythagorean Identities | |

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Quotient Identities | |

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Summary | |

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Review Exercises | |

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Test | |

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Quantitative Reasoning | |

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Acute Angles and Right Triangles | |

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Trigonometric Functions of Acute Angles | |

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Right-Triangle-Based Definitions of the Trigonometric Functions | |

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Cofunctions | |

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Trigonometric Function Values of Special Angles | |

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Trigonometric Functions of Non-Acute Angles | |

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Reference Angles | |

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Special Angles as Reference Angles | |

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Finding Angle Measures with Special Angles | |

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Finding Trigonometric Function Values Using a Calculator | |

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Finding Function Values Using a Calculator | |

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Finding Angle Measures Using a Calculator | |

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Solving Right Triangles | |

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Significant Digits | |

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Solving Triangles | |

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Angles of Elevation or Depression | |

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Further Applications of Right Triangles | |

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Bearing | |

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Further Applications | |

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Summary | |

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Review Exercises | |

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Test | |

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Quantitative Reasoning | |

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Radian Measure and Circular Functions | |

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Radian Measure | |

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Radian Measure | |

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Converting Between Degrees and Radians | |

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Finding Function Values for Angles in Radians | |

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Applications of Radian Measure | |

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Arc Length on a Circle | |

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Area of a Sector of a Circle | |

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The Unit Circle and Circular Functions | |

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Circular Functions | |

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Finding Values of Circular Functions | |

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Determining a Number with a Given Circular Function Value | |

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Applying Circular Functions | |

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Linear and Angular Speed | |

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Linear Speed | |

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Angular Speed | |

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Summary | |

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Review Exercises | |

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Test | |

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Quantitative Reasoning | |

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Graphs of the Circular Functions | |

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Graphs of the Sine and Cosine Functions | |

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Periodic Functions | |

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Graph of the Sine Function | |

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Graph of the Cosine Function | |

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Graphing Techniques, Amplitude, and Period | |

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Using a Trigonometric Model | |

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Translations of the Graphs of the Sine and Cosine Functions | |

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Horizontal Translations | |

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Vertical Translations | |

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Combinations of Translations | |

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Determining a Trigonometric Model Using Curve Fitting | |

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Graphs of the Other Circular Functions | |

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Graphs of the Cosecant and Secant Functions | |

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Graphs of the Tangent and Cotangent Functions | |

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Addition of Ordinates | |

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Summary Exercises on Graphing Circular Functions | |

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Harmonic Motion | |

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Simple Harmonic Motion | |

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Damped Oscillatory Motion | |

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Summary | |

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Review Exercises | |

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Test | |

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Quantitative Reasoning | |

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Trigonometric Identities | |

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Fundamental Identities | |

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Negative-Angle Identities | |

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Fundamental Identities | |

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Using the Fundamental Identities | |

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Verifying Trigonometric Identities | |

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Verifying Identities by Working with One Side | |

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Verifying Identities by Working with Both Sides | |

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Sum and Difference Identities for Cosine | |

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Difference Identity for Cosine | |

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Sum Identity for Cosine | |

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Cofunction Identities | |

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Applying the Sum and Difference Identities | |

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Sum and Difference Identities for Sine and Tangent | |

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Sum and Difference Identities for Sine | |

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Sum and Difference Identities for Tangent | |

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Applying the Sum and Difference Identities | |

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Double-Angle Identities | |

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Double-Angle Identities | |

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Product-to-Sum and Sum-to-Product Identities | |

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Half-Angle Identities | |

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Half-Angle Identities | |

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Applying the Half-Angle Identities | |

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Summary Exercises on Verifying Trigonometric Identities | |

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Summary | |

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Review Exercises | |

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Test | |

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Quantitative Reasoning | |

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Inverse Circular Functions and Trigonometric Equations | |

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Inverse Circular Functions | |

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Inverse Functions | |

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Inverse Sine Function | |

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Inverse Cosine Function | |

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Inverse Tangent Function | |

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Remaining Inverse Circular Functions | |

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Inverse Function Values | |

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Trigonometric Equations I | |

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Solving by Linear Methods | |

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Solving by Factoring | |

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Solving by Quadratic Methods | |

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Solving by Using Trigonometric Identities | |

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Trigonometric Equations II | |

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Equations with Half-Angles | |

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Equations with Multiple Angles | |

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Equations Involving Inverse Trigonometric Functions | |

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Solving for x in Terms of y Using Inverse Functions | |

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Solving Inverse Trigonometric Equations | |

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Summary | |

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Review Exercises | |

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Test | |

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Quantitative Reasoning | |

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Applications of Trigonometry and Vectors | |

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Oblique Triangles and the Law of Sines | |

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Congruency and Oblique Triangles | |

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Derivation of the Law of Sines | |

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Solving SAA and ASA Triangles (Case 1) | |

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Area of a Triangle | |

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The Ambiguous Case of the Law of Sines | |

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Description of the Ambiguous Case | |

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Solving SSA Triangles (Case 2) | |

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Analyzing Data for Possible Number of Triangles | |

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The Law of Cosines | |

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Derivation of the Law of Cosines | |

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Solving SAS and SSS Triangles (Cases 3 and 4) | |

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Heron's Formula for the Area of a Triangle | |

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Vectors, Operations, and the Dot Product | |

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Basic Terminology | |

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Algebraic Interpretation of Vectors | |

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Operations with Vectors | |

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Dot Product and the Angle Between Vectors | |

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Applications of Vectors | |

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The Equilibrant | |

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Incline Applications | |

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Navigation Applications | |

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Summary | |

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Review Exercises | |

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Test | |

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Quantitative Reasoning | |

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Complex Numbers, Polar Equations, and Parametric Equations | |

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Complex Numbers | |

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Basic Concepts of Complex Numbers | |

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Complex Solutions of Equations | |

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Operations on Complex Numbers | |

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Trigonometric (Polar) Form of Complex Numbers | |

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The Complex Plane and Vector Representation | |

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Trigonometric (Polar) Form | |

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Converting Between Trigonometric and Polar Forms | |

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An Application of Complex Numbers to Fractals | |

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The Product and Quotient Theorems | |

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Products of Complex Numbers in Trigonometric Form | |

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Quotients of Complex Numbers in Trigonometric Form | |

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De Moivre's Theorem; Powers and Roots of Complex Numbers | |

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Powers of Complex Numbers (De Moivre's Theorem) | |

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Roots of Complex Numbers | |

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Polar Equations and Graphs | |

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Polar Coordinate System | |

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Graphs of Polar Equations | |

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Converting from Polar to Rectangular Equations | |

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Classifying Polar Equations | |

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Parametric Equations, Graphs, and Applications | |

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Basic Concepts | |

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Parametric Graphs and Their Rectangular Equivalents | |

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The Cycloid | |

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Applications of Parametric Equations | |

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Summary | |

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Review Exercises | |

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Test | |

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Quantitative Reasoning | |

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Exponential and Logarithmic Functions | |

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Exponential Functions | |

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Exponents and Properties | |

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Exponential Functions | |

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Exponential Equations | |

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Compound Interest | |

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The Number e and Continuous Compounding | |

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Exponential Models and Curve Fitting | |

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Logarithmic Functions | |

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Logarithms | |

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Logarithmic Equations | |

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Logarithmic Functions | |

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Properties of Logarithms | |

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Evaluating Logarithms; Equations and Applications | |

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Common Logarithms | |

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Natural Logarithms | |

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Logarithms to Other Bases | |

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Exponential and Logarithmic Equations | |

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Summary | |

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Review Exercises | |

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Test | |

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Quantitative Reasoning | |

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Equations and Inequalities | |

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Equations | |

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Solving Linear Equations | |

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Solving Quadratic Equations | |

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Inequalities | |

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Solving Linear Inequalities | |

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Interval Notation | |

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Three-Part Inequalities | |

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Graphs of Equations | |

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The Rectangular Coordinate System | |

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The Pythagorean Theorem and the Distance Formula | |

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The Midpoint Formula | |

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Graphing Equations | |

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Circles | |

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Functions | |

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Relations and Functions | |

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Domain and Range | |

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Determining Whether a Relation Is a Function | |

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Function Notation | |

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Increasing, Decreasing, and Constant Functions | |

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Graphing Techniques | |

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Stretching and Shrinking | |

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Reflecting | |

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Symmetry | |

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Translations | |

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Glossary | |

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Solutions to Selected Exercises | |

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Answers to Selected Exercises | |

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Index of Applications | |

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Index | |