Algebra & Trigonometry

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Cover Page Chapter Review Features To the Student Dedication Page Title Page Copyright Page CONTENTS Three Distinct Series Preface to the Instructor Student Resources Applications Index Photo Credits R: Review R.1 Real Numbers R.2 Algebra Essentials R.3 Geometry Essentials R.4 Polynomials R.5 Factoring Polynomials R.6 Synthetic Division R.7 Rational Expressions R.8 nth Roots; Rational Exponents 1 Equations and Inequalities 1.1 Linear Functions 1.2 Quadratic Equations 1.3 Complex Numbers; Quadratic Equations in the Complex Number System 1.4 Radical Equations;Equations Quadratic in Form; Factorable Equations 1.5 Solving Inequalities 1.6 Equations and Inequalities Involving Absolute Value 1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications Chapter Review Chapter Test Chapter Projects 2 Graphs 2.1 The Distance and Midpoint Formulas 2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry 2.3 Lines 2.4 Circles 2.5 Variation Chapter Review Chapter Test Cumulative Review Chapter Project 3 Functions and Their Graphs 3.1 Functions 3.2 The Graph of a Function 3.3 Properties of Functions 3.4 Library of Functions; Piecewise-defined Functions 3.5 Graphing Techniques:Transformations 3.6 Mathematical Models: Building Functions Chapter Review Chapter Test Cumulative Review Chapter Projects 4 Linear and Quadratic Functions 4.1 Linear Functions and Their Properties 4.2 Linear Models: Building Linear Functions from Data 4.3 Quadratic Functions and Their Properties 4.4 Build Quadratic Models from Verbal Descriptions and from Data 4.5 Inequalities Involving Quadratic Functions Chapter Review Chapter Test Cumulative Review Chapter Projects 5 Polynomial and Rational Functions 5.1 Polynomial Functions and Models 5.2 Properties of Rational Functions 5.3 The Graph of a Rational Function 5.4 Polynomial and Rational Inequalities 5.5 The Real Zeros of a Polynomial Function 5.6 Complex Zeros; Fundamental Theorem of Algebra Chapter Review Chapter Test Cumulative Review Chapter Projects 6 Exponential and Logarithmic Functions 6.1 Composite Functions 6.2 One-to-One Functions; Inverse Functions 6.3 Exponential Functions 6.4 Logarithmic Functions 6.5 Properties of Logarithms 6.6 Logarithmic and Exponential Equations 6.7 Financial Models 6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models 6.9 Building Exponential, Logarithmic, and Logistic Models from Data Chapter Review Chapter Test Cumulative Review Chapter Projects 7 Trigonometric Functions 7.1 Angles and Their Measure 7.2 Right Triangle Trigonometry 7.3 Computing the Values of Trigonometric Functions of Acute Angles 7.4 Trigonometric Functions of Any Angle 7.5 Unit Circle Approach; Properties of the Trigonometric Functions 7.6 Graphs of the Sine and Cosine Functions 7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 7.8 Phase Shift; Sinusoidal Curve Fitting Chapter Review Chapter Test Cumulative Review Chapter Projects 8 Analytic Trigonometry 8.1 The Inverse Sine, Cosine, and Tangent Functions 8.2 The Inverse Trigonometric Functions (Continued) 8.3 Trigonometric Equations 8.4 Trigonometric Identities 8.5 Sum and Difference Formulas 8.6 Double-angle and Half-angle Formulas 8.7 Product-to-Sum and Sum-to-Product Formulas Chapter Review Chapter Test Cumulative Review Chapter Projects 9 Applications of Trigonometric Functions 9.1 Applications Involving Right Triangles 9.2 The Law of Sines 9.3 The Law of Cosines 9.4 Area of a Triangle 9.5 Simple Harmonic Motion; Damped Motion; Combining Waves Chapter Review Chapter Test Cumulative Review Chapter Projects 10 Polar Coordinates;Vectors 10.1 Polar Coordinates 10.2 Polar Equations and Graphs 10.3 The Complex Plane; De Moivre’s Theorem 10.4 Vectors 10.5 The Dot Product Chapter Review Chapter Test Cumulative Review Chapter Projects 11 Analytic Geometry 11.1 Conics 11.2 The Parabola 11.3 The Ellipse 11.4 The Hyperbola 11.5 Rotation of Axes; General Form of a Conic 11.6 Polar Equations of Conics 11.7 Plane Curves and Parametric Equations Chapter Review Chapter Test Cumulative Review Chapter Projects 12 Systems of Equations and Inequalities 12.1 Systems of Linear Equations: Substitution and Elimination 12.2 Systems of Linear Equations: Matrices 12.3 Systems of Linear Equations: Determinants 12.4 Matrix Algebra 12.5 Partial Fraction Decomposition 12.6 Systems of Nonlinear Equations 12.7 Systems of Inequalities 12.8 Linear Programming Chapter Review Chapter Test Cumulative Review Chapter Projects 13 Sequences; Induction; the Binomial Theorem 13.1 Sequences 13.2 Arithmetic Sequences 13.3 Geometric Sequences; Geometric Series 13.4 Mathematical Induction 13.5 The Binomial Theorem Chapter Review Chapter Test Cumulative Review Chapter Projects 14 Counting and Probability 14.1 Counting 14.2 Permutations and Combinations 14.3 Probability Chapter Review Chapter Test Cumulative Review Chapter Projects APPENDIX: Graphing Utilities 1 The Viewing Rectangle 2 Using a Graphing Utility to Graph Equations 3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry 4 Using a Graphing Utility to Solve Equations 5 Square Screens 6 Using a Graphing Utility to Graph Inequalities 7 Using a Graphing Utility to Solve Systems of Linear Equations 8 Using a Graphing Utility to Graph a Polar Equation 9 Using a Graphing Utility to Graph Parametric Equations Answers INDEX Prepare for Class... Practice... Info Sheets