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This title in other editionsStudent's Solutions Manual for Precalculus: Concepts Through Functions, a Right Triangle Approach to Trigonometryby Michael Sullivan
Synopses & ReviewsPublisher Comments: Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry, Second Edition embodies Sullivan/Sullivan’s hallmarks–accuracy, precision, depth, strong student support, and abundant exercises–while exposing readers to functions in the first chapter. To ensure that students master basic skills and develop the conceptual understanding they need for the course, this text focuses on the fundamentals: preparing for class, practicing their homework, and reviewing the concepts. After using this book, students will have a solid understanding of algebra and functions so that they are prepared for subsequent courses, such as finite mathematics, business mathematics, and engineering calculus.
KEY TOPICS: Functions and Their Graphs; Linear and Quadratic Functions; Polynomial and Rational Functions; Exponential and Logarithmic Functions; Trigonometric Functions; Analytic Trigonometry; Applications of Trigonometric Functions; Polar Coordinates; Vectors; Analytic Geometry; Systems of Equations and Inequalities; Sequences; Induction; the Binomial Theorem; Counting and Probability; A Preview of Calculus: The Limit; Derivative, and Integral of a Function MARKET: For all readers interested in precalculus. About the AuthorMike Sullivan is Professor of Mathematics at Chicago State University, having taught there for more than 30 years. He received his PhD in mathematics from Illinois Institute of Technology. He is a native of Chicago’s South Side and currently resides in Oak Lawn, Illinois. Mike has four children; the two oldest have degrees in mathematics and assisted in proofing, checking examples and exercises, and writing solutions manuals for this project. His son, Mike Sullivan, III, coauthored the Sullivan Graphing with Data Analysis series as well as this series. Mike has authored or coauthored more than ten books. He owns a travel agency, and splits his time between a condo in Naples, Florida and a home in Oak Lawn, where Mike enjoys gardening. Mike Sullivan, III is a professor of mathematics at Joliet Junior College. He holds graduate degrees from DePaul University in both mathematics and economics. Mike is an author or coauthor on more than 20 books, including a statistics book and a developmental mathematics series. Mike is the father of three children and an avid golfer who tries to spend as much of his limited free time as possible on the golf course. Table of ContentsFoundations: 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
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; Piecewisedefined Functions 1.5 Graphing Techniques: Transformations 1.6 Mathematical Models: Constructing 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 Chapter Projects Cumulative Review
3. Polynomial and Rational Functions 3.1 Polynomial Functions and Models 3.2 Properties of Rational Functions 3.3 The Graph of a Rational Function 3.4 Polynomial and Rational Inequalities 3.5 The Real Zeros of a Polynomial Function 3.6 Complex Zeros; Fundamental Theorem of Algebra Chapter Review Chapter Test Chapter Projects Cumulative Review
4. Exponential and Logarithmic Functions 4.1 Composite Functions 4.2 OnetoOne Functions; Inverse Functions 4.3 Exponential Functions 4.4 Logarithmic Functions 4.5 Properties of Logarithms 4.6 Logarithmic and Exponential Equations 4.7 Compound Interest 4.8 Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay 4.9 Building Exponential, Logarithmic, and Logistic Functions from Data Chapter Review Chapter Test Chapter Projects Cumulative Review
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 General Angles 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 Chapter Projects Cumulative Review
6. Analytic Trigonometry 6.1 The Inverse Sine, Cosine, and Tangent Functions 6.2 The Inverse Trigonometric Functions (Continued) 6.3 Trigonometric Identities 6.4 Sum and Difference Formulas 6.5 Doubleangle and Halfangle Formulas 6.6 ProducttoSum and SumtoProduct Formulas 6.7 Trigonometric Equations Chapter Review Chapter Test Chapter Projects Cumulative Review
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 Chapter Projects Cumulative Review
8. Polar Coordinates; Vectors 8.1 Polar Coordinates 8.2 Polar Equations and Graphs 8.3 The Complex Plane; DeMoivre's Theorem 8.4 Vectors 8.5 The Dot Product 8.6 Vectors in Space 8.7 The Cross Product Chapter Review Chapter Test Chapter Projects Cumulative Review
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 Chapter Projects Cumulative Review
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 Chapter Projects Cumulative Review
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 Chapter Projects Cumulative Review
12. Counting and Probability 12.1 Counting 12.2 Permutations and Combinations 12.3 Probability Chapter Review Chapter Test Chapter Projects Cumulative Review
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 Onesided Limits; Continuous Functions 13.4 The Tangent Problem; The Derivative 13.5 The Area Problem; The Integral Chapter Review Chapter Test Chapter Projects Cumulative Review
Appendix 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 Jobs A.10 Interval Notation; Solving Inequalities A.11 Complex Numbers
Appendix 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
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