Precalculus : concepts through functions : a right triangle approach to trigonometry
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Cover Title Page Copyright Page Contents To the Student Three Distinct Series The Concepts through Functions Series Preface to the Instructor Applications Index F. Foundations: A Prelude to Functions F.1. The Distance and Midpoint Formulas F.2. Graphs of Equations in Two Variables; Intercepts; Symmetry F.3. Lines F.4. Circles Chapter Project 1. Functions and Their Graphs 1.1. Functions 1.2. The Graph of a Function 1.3. Properties of Functions 1.4. Library of Functions; Piecewise-defined Functions 1.5. Graphing Techniques: Transformations 1.6. Mathematical Models: Building Functions 1.7. Building Mathematical Models Using Variation Chapter Review Chapter Test Chapter Projects 2. Linear and Quadratic Functions 2.1. Properties of Linear Functions and Linear Models 2.2. Building Linear Models from Data 2.3. Quadratic Functions and Their Zeros 2.4. Properties of Quadratic Functions 2.5. Inequalities Involving Quadratic Functions 2.6. Building Quadratic Models from Verbal Descriptions and from Data 2.7. Complex Zeros of a Quadratic Function 2.8. Equations and Inequalities Involving the Absolute Value Function Chapter Review Chapter Test Cumulative Review Chapter Projects 3. Polynomial and Rational Functions 3.1. Polynomial Functions and Models 3.2. The Real Zeros of a Polynomial Function 3.3. Complex Zeros; Fundamental Theorem of Algebra 3.4. Properties of Rational Functions 3.5. The Graph of a Rational Function 3.6. Polynomial and Rational Inequalities Chapter Review Chapter Test Cumulative Review Chapter Projects 4. Exponential and Logarithmic Functions 4.1. Composite Functions 4.2. One-to-One Functions; Inverse Functions 4.3. Exponential Functions 4.4. Logarithmic Functions 4.5. Properties of Logarithms 4.6. Logarithmic and Exponential Equations 4.7. Financial Models 4.8. Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models 4.9. Building Exponential, Logarithmic, and Logistic Models from Data Chapter Review Chapter Test Cumulative Review Chapter Projects 5. Trigonometric Functions 5.1. Angles and Their Measure 5.2. Right Triangle Trigonometry 5.3. Computing the Values of Trigonometric Functions of Acute Angles 5.4. Trigonometric Functions of any Angle 5.5. Unit Circle Approach; Properties of the Trigonometric Functions 5.6. Graphs of the Sine and Cosine Functions 5.7. Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 5.8. Phase Shift; Sinusoidal Curve Fitting Chapter Review Chapter Test Cumulative Review Chapter Projects 6. Analytic Trigonometry 6.1. The Inverse Sine, Cosine, and Tangent Functions 6.2. The Inverse Trigonometric Functions (Continued) 6.3. Trigonometric Equations 6.4. Trigonometric Identities 6.5. Sum and Difference Formulas 6.6. Double-angle and Half-angle Formulas 6.7. Product-to-Sum and Sum-to-Product Formulas Chapter Review Chapter Test Cumulative Review Chapter Projects 7. Applications of Trigonometric Functions 7.1. Applications Involving Right Triangles 7.2. The Law of Sines 7.3. The Law of Cosines 7.4. Area of a Triangle 7.5. Simple Harmonic Motion; Damped Motion; Combining Waves Chapter Review Chapter Test Cumulative Review Chapter Projects 8. Polar Coordinates; Vectors 8.1. Polar Coordinates 8.2. Polar Equations and Graphs 8.3. The Complex Plane; De Moivre’s Theorem 8.4. Vectors 8.5. The Dot Product 8.6. Vectors in Space 8.7. The Cross Product Chapter Review Chapter Test Cumulative Review Chapter Projects 9. Analytic Geometry 9.1. Conics 9.2. The Parabola 9.3. The Ellipse 9.4. The Hyperbola 9.5. Rotation of Axes; General Form of a Conic 9.6. Polar Equations of Conics 9.7. Plane Curves and Parametric Equations Chapter Review Chapter Test Cumulative Review Chapter Projects 10. Systems of Equations and Inequalities 10.1. Systems of Linear Equations: Substitution and Elimination 10.2. Systems of Linear Equations: Matrices 10.3. Systems of Linear Equations: Determinants 10.4. Matrix Algebra 10.5. Partial Fraction Decomposition 10.6. Systems of Nonlinear Equations 10.7. Systems of Inequalities 10.8. Linear Programming Chapter Review Chapter Test Cumulative Review Chapter Projects 11. Sequences; Induction; the Binomial Theorem 11.1. Sequences 11.2. Arithmetic Sequences 11.3. Geometric Sequences; Geometric Series 11.4. Mathematical Induction 11.5. The Binomial Theorem Chapter Review Chapter Test Cumulative Review Chapter Projects 12. Counting and Probability 12.1. Counting 12.2. Permutations and Combinations 12.3. Probability Chapter Review Chapter Test Cumulative Review Chapter Projects 13. A Preview of Calculus: The Limit, Derivative, and Integral of a Function 13.1. Finding Limits Using Tables and Graphs 13.2. Algebra Techniques for Finding Limits 13.3. One-sided Limits; Continuous Functions 13.4. The Tangent Problem; The Derivative 13.5. The Area Problem; The Integral Chapter Review Chapter Test Chapter Projects A. Review A.1. Algebra Essentials A.2. Geometry Essentials A.3. Polynomials A.4. Factoring Polynomials A.5. Synthetic Division A.6. Rational Expressions A.7. nth Roots; Rational Exponents A.8. Solving Equations A.9. Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications A.10. Interval Notation; Solving Inequalities A.11. Complex Numbers B. Graphing Utilities B.1. The Viewing Rectangle B.2. Using a Graphing Utility to Graph Equations B.3. Using a Graphing Utility to Locate Intercepts and Check for Symmetry B.4. Using a Graphing Utility to Solve Equations B.5. Square Screens B.6. Using a Graphing Utility to Graph Inequalities B.7. Using a Graphing Utility to Solve Systems of Linear Equations B.8. Using a Graphing Utility to Graph a Polar Equation B.9. Using a Graphing Utility to Graph Parametric Equations Answers Subject Index Photo Credits Conics Library of Functions Formulas/Equations Geometry Formulas Trignometric Functions Trignometric Identities Back Cover
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