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# Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry

**by**Sullivan, Michael; Sullivan III, Michael

### 9780131874763

0131874764

Hardcover

1/1/2007

Prentice Hall

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## Summary

This new text embodies Sullivan/Sullivanrs"s hallmarks - accuracy, precision, depth, strong student support, and abundant exerciseswhile exposing students early (Chapter One) to the study of functionsand taking aright triangle approachto trigonometry."IT WORKS"for instructors and students because it focuses students on thefundamentals:preparingfor class,practicingtheir homework, andreviewing. After completing the book, students will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engineering calculus and will have a solid understanding of the concept of a function.

## Table of Contents

Preface to the Instructor | p. xiii |

List of Applications | p. xix |

Photo Credits | p. xxiii |

To the Student | p. xxiv |

Foundations: A Prelude To Functions | p. 1 |

The Distance and Midpoint Formulas | p. 2 |

Graphs of Equations in Two Variables; Intercepts; Symmetry | p. 8 |

Lines | p. 18 |

Circles | p. 33 |

Functions and Their Graphs | p. 39 |

Functions | p. 40 |

The Graph of a Function | p. 54 |

Properties of Functions | p. 63 |

Library of Functions; Piecewise-defined Functions | p. 75 |

Graphing Techniques: Transformations | p. 85 |

Mathematical Models: Constructing Functions | p. 97 |

Chapter Review | p. 105 |

Chapter Test | p. 111 |

Chapter Projects | p. 112 |

Linear and Quadratic Functions | p. 113 |

Properties of Linear Functions | p. 114 |

Building Linear Functions from Data; Direct Variation | p. 125 |

Quadratic Functions and Their Zeros | p. 133 |

Properties of Quadratic Functions | p. 144 |

Inequalities Involving Quadratic Functions | p. 154 |

Quadratic Models | p. 158 |

Complex Zeros of a Quadratic Function | p. 167 |

Equations and Inequalities Involving the Absolute Value Function | p. 170 |

Chapter Review | p. 175 |

Chapter Test | p. 179 |

Chapter Projects | p. 179 |

Cumulative Review | p. 180 |

Polynomial and Rational Functions | p. 181 |

Polynomial Functions and Models | p. 182 |

Properties of Rational Functions | p. 203 |

The Graph of a Rational Function; Inverse and Joint Variation | p. 213 |

Polynomial and Rational Inequalities | p. 231 |

The Real Zeros of a Polynomial Function | p. 236 |

Complex Zeros; Fundamental Theorem of Algebra | p. 250 |

Chapter Review | p. 256 |

Chapter Test | p. 259 |

Chapter Projects | p. 260 |

Cumulative Review | p. 261 |

Exponential and Logarithmic Functions | p. 263 |

Composite Functions | p. 264 |

One-to-One Functions; Inverse Functions | p. 271 |

Exponential Functions | p. 284 |

Logarithmic Functions | p. 300 |

Properties of Logarithms | p. 312 |

Logarithmic and Exponential Equations | p. 320 |

Compound Interest | p. 325 |

Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay | p. 334 |

Building Exponential, Logarithmic, and Logistic Functions from Data | p. 345 |

Chapter Review | p. 353 |

Chapter Test | p. 359 |

Chapter Projects | p. 359 |

Cumulative Review | p. 360 |

Trigonometric Functions | p. 361 |

Angles and Their Measure | p. 362 |

Right Triangle Trigonometry | p. 375 |

Computing the Values of Trigonometric Functions of Acute Angles | p. 386 |

Trigonometric Functions of General Angles | p. 397 |

Unit Circle Approach; Properties of the Trigonometric Functions | p. 407 |

Graphs of the Sine and Cosine Functions | p. 418 |

Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions | p. 433 |

Phase Shift; Sinusoidal Curve Fitting | p. 439 |

Chapter Review | p. 450 |

Chapter Test | p. 456 |

Chapter Projects | p. 457 |

Cumulative Review | p. 458 |

Analytic Trigonometry | p. 459 |

The Inverse Sine, Cosine, and Tangent Functions | p. 460 |

The Inverse Trigonometric Functions (Continued) | p. 472 |

Trigonometric Identities | p. 477 |

Sum and Difference Formulas | p. 485 |

Double-angle and Half-angle Formulas | p. 494 |

Product-to-Sum and Sum-to-Product Formulas | p. 503 |

Trigonometric Equations (I) | p. 507 |

Trigonometric Equations (II) | p. 613 |

Chapter Review | p. 520 |

Chapter Test | p. 524 |

Chapter Projects | p. 524 |

Cumulative Review | p. 525 |

Applications of Trigonometric Functions | p. 527 |

Applications Involving Right Triangles | p. 528 |

The Law of Sines | p. 533 |

The Law of Cosines | p. 544 |

Area of a Triangle | p. 550 |

Simple Harmonic Motion; Damped Motion; Combining Waves | p. 555 |

Chapter Review | p. 564 |

Chapter Test | p. 568 |

Chapter Projects | p. 569 |

Cumulative Review | p. 570 |

Polar Coordinates; Vectors | p. 571 |

Polar Coordinates | p. 572 |

Polar Equations and Graphs | p. 580 |

The Complex Plane; De Moivre's Theorem | p. 596 |

Vectors | p. 604 |

The Dot Product | p. 615 |

Vectors in Space | p. 623 |

The Cross Product | p. 632 |

Chapter Review | p. 638 |

Chapter Test | p. 642 |

Chapter Projects | p. 643 |

Cumulative Review | p. 644 |

Analytic Geometry | p. 645 |

Conics | p. 646 |

The Parabola | p. 647 |

The Ellipse | p. 656 |

The Hyperbola | p. 666 |

Rotation of Axes; General Form of a Conic | p. 678 |

Polar Equations of Conics | p. 686 |

Plane Curves and Parametric Equations | p. 692 |

Chapter Review | p. 704 |

Chapter Test | p. 707 |

Chapter Projects | p. 707 |

Cumulative Review | p. 708 |

Systems of Equations and Inequalities | p. 709 |

Systems of Linear Equations: Substitution and Elimination | p. 710 |

Systems of Linear Equations: Matrices | p. 724 |

Systems of Linear Equations: Determinants | p. 739 |

Matrix Algebra | p. 749 |

Partial Fraction Decomposition | p. 765 |

Systems of Nonlinear Equations | p. 772 |

Systems of Inequalities | p. 781 |

Linear Programming | p. 789 |

Chapter Review | p. 796 |

Chapter Test | p. 801 |

Chapter Projects | p. 802 |

Cumulative Review | p. 803 |

Sequences; Induction; The Binomial Theorem | p. 805 |

Sequences | p. 806 |

Arithmetic Sequences | p. 815 |

Geometric Sequences; Geometric Series | p. 820 |

Mathematical Induction | p. 831 |

The Binomial Theorem | p. 834 |

Chapter Review | p. 841 |

Chapter Test | p. 843 |

Chapter Projects | p. 844 |

Cumulative Review | p. 844 |

Counting and Probability | p. 895 |

Sets and Counting | p. 846 |

Permutations and Combinations | p. 851 |

Probability | p. 861 |

Chapter Review | p. 871 |

Chapter Test | p. 874 |

Chapter Projects | p. 875 |

Cumulative Review | p. 875 |

A Preview of Calculus: The Limit, Derivative, and Integral of a Function | p. 877 |

Finding Limits Using Tables and Graphs | p. 878 |

Algebra Techniques for Finding Limits | p. 883 |

One-sided Limits; Continuous Functions | p. 890 |

The Tangent Problem; The Derivative | p. 897 |

The Area Problem; The Integral | p. 905 |

Chapter Review | p. 911 |

Chapter Test | p. 915 |

Chapter Projects | p. 916 |

Review | p. 1 |

Algebra Essentials | p. 1 |

Geometry Essentials | p. 11 |

Polynomials | p. 19 |

Factoring Polynomials | p. 29 |

Synthetic Division | p. 38 |

Rational Expressions | p. 41 |

nth Roots; Rational Exponents | p. 52 |

Solving Equations | p. 60 |

Interval Notation; Solving Inequalities | p. 66 |

Problem Solving: Applications of Linear Equations | p. 74 |

Complex Numbers | p. 82 |

Graphing Utilities | p. 1 |

The Viewing Rectangle | p. 1 |

Using a Graphing Utility to Graph Equations | p. 3 |

Using a Graphing Utility to Locate Intercepts and Check for Symmetry | p. 7 |

Using a Graphing Utility to Solve Equations | p. 9 |

Square Screens | p. 11 |

Using a Graphing Utility to Graph Inequalities | p. 12 |

Using a Graphing Utility to Solve Systems of Linear Equations | p. 14 |

Using a Graphing Utility to Graph a Polar Equation | p. 15 |

Using a Graphing Utility to Graph Parametric Equations | p. 16 |

Answers | p. 1 |

Index | p. 1 |

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