Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

Description

For courses in precalculus. Ties concepts together using a functions approach The Concepts Through Functions Series introduces functions at the start of each text, and maintains a continuous theme by introducing/developing a new function in every chapter. Known for their ability to connect with today’s students, acclaimed authors Sullivan and Sullivan focus on the fundamentals – preparing for class, practice with homework, and reviewing key concepts – encouraging students to master basic skills and develop the conceptual understanding needed for this and future courses. Graphing utility coverage is optional, and can be included at the discretion of each instructor based on course needs. Also available with MyLab Math MyLabTM Math is the teaching and learning platform that empowers instructors to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for each student. 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If you would like to purchase both the physical text and MyLab Math, search for: 0134859049 / 9780134859040 Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry Plus MyLab Math with eText -- Title-Specific Access Card Package, 4/e Package consists of: 0134686977 / 9780134686974 Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry0134852214 / 9780134852218 MyLab Math with Pearson eText - Standalone Access Card - for Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry 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 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. Trigonometric Functions: Unit Circle Approach 5.3. Properties of the Trigonometric Functions 5.4. Graphs of the Sine and Cosine Functions 5.5. Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions 5.6. 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. Right Triangle Trigonometry; Applications 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 Photo Credits Subject Index Conics Library of Functions Formulas/Equations Trigonometric Functions Back Cover