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# Algebra and Trigonometry with Analytic Geometry, Classic Edition (with CD-ROM and iLrn™)

**by**Swokowski, Earl; Cole, Jeffery A.

11th

### 9780534404697

0534404693

Hardcover

3/30/2005

Brooks Cole

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## Summary

This latest edition in the highly respected Swokowski/Cole precalculus series retains the elements that have made it so popular with instructors and students alike: its exposition is clear, the time-tested exercise sets feature a variety of applications, its uncluttered layout is appealing, and the difficulty level of problems is appropriate and consistent. The goal of this text is to prepare students for further courses in mathematics. Mathematically sound, ALGEBRA AND TRIGONOMETRY WITH ANALYTIC GEOMETRY (CLASSIC EDITION), Eleventh Edition, effectively prepares students for further courses in mathematics through its excellent, time-tested problem sets.

## Table of Contents

Preface | p. viii |

Fundamental Concepts of Algebra | p. 1 |

Real Numbers | p. 2 |

Exponents and Radicals | p. 16 |

Algebraic Expressions | p. 27 |

Fractional Expressions | p. 40 |

Chapter 1 Review Exercises | p. 49 |

Chapter 1 Discussion Exercises | p. 51 |

Equations and Inequalities | p. 53 |

Equations | p. 54 |

Applied Problems | p. 61 |

Quadratic Equations | p. 73 |

Complex Numbers | p. 87 |

Other Types of Equations | p. 94 |

Inequalities | p. 102 |

More on Inequalities | p. 111 |

Chapter 2 Review Exercises | p. 119 |

Chapter 2 Discussion Exercises | p. 122 |

Functions and Graphs | p. 123 |

Rectangular Coordinate Systems | p. 124 |

Graphs of Equations | p. 130 |

Lines | p. 140 |

Definition of Function | p. 155 |

Graphs of Functions | p. 171 |

Quadratic Functions | p. 185 |

Operations on Functions | p. 197 |

Chapter 3 Review Exercises | p. 205 |

Chapter 3 Discussion Exercises | p. 210 |

Polynomial and Rational Functions | p. 213 |

Polynomial Functions of Degree Greater Than 2 | p. 214 |

Properties of Division | p. 222 |

Zeros of Polynomials | p. 229 |

Complex and Rational Zeros of Polynomials | p. 241 |

Rational Functions | p. 248 |

Variation | p. 265 |

Chapter 4 Review Exercises | p. 272 |

Chapter 4 Discussion Exercises | p. 275 |

Inverse, Exponential, and Logarithmic Functions | p. 277 |

Inverse Functions | p. 278 |

Exponential Functions | p. 287 |

The Natural Exponential Function | p. 299 |

Logarithmic Functions | p. 308 |

Properties of Logarithms | p. 323 |

Exponential and Logarithmic Equations | p. 330 |

Chapter 5 Review Exercises | p. 342 |

Chapter 5 Discussion Exercises | p. 345 |

The Trigonometric Functions | p. 347 |

Angles | p. 348 |

Trigonometric Functions of Angles | p. 358 |

Trigonometric Functions of Real Numbers | p. 375 |

Values of the Trigonometric Functions | p. 393 |

Trigonometric Graphs | p. 400 |

Additional Trigonometric Graphs | p. 412 |

Applied Problems | p. 420 |

Chapter 6 Review Exercises | p. 433 |

Chapter 6 Discussion Exercises | p. 439 |

Analytic Trigonometry | p. 441 |

Verifying Trigonometric Identities | p. 442 |

Trigonometric Equations | p. 447 |

The Addition and Subtraction Formulas | p. 457 |

Multiple-Angle Formulas | p. 467 |

Product-to-Sum and Sum-to-Product Formulas | p. 477 |

The Inverse Trigonometric Functions | p. 482 |

Chapter 7 Review Exercises | p. 496 |

Chapter 7 Discussion Exercises | p. 499 |

Applications of Trigonometry | p. 501 |

The Law of Sines | p. 502 |

The Law of Cosines | p. 512 |

Vectors | p. 522 |

The Dot Product | p. 536 |

Trigonometric Form for Complex Numbers | p. 546 |

De Moivre's Theorem and nth Roots of Complex Numbers | p. 552 |

Chapter 8 Review Exercises | p. 557 |

Chapter 8 Discussion Exercises | p. 560 |

Systems of Equations and Inequalities | p. 563 |

Systems of Equations | p. 564 |

Systems of Linear Equations in Two Variables | p. 573 |

Systems of Inequalities | p. 582 |

Linear Programming | p. 590 |

Systems of Linear Equations in More Than Two Variables | p. 598 |

The Algebra of Matrices | p. 614 |

The Inverse of a Matrix | p. 623 |

Determinants | p. 628 |

Properties of Determinants | p. 634 |

Partial Fractions | p. 642 |

Chapter 9 Review Exercises | p. 648 |

Chapter 9 Discussion Exercises | p. 651 |

Sequences, Series, and Probability | p. 653 |

Infinite Sequences and Summation Notation | p. 654 |

Arithmetic Sequences | p. 664 |

Geometric Sequences | p. 671 |

Mathematical Induction | p. 680 |

The Binomial Theorem | p. 686 |

Permutations | p. 695 |

Distinguishable Permutations and Combinations | p. 702 |

Probability | p. 709 |

Chapter 10 Review Exercises | p. 723 |

Chapter 10 Discussion Exercises | p. 725 |

Topics from Analytic Geometry | p. 727 |

Parabolas | p. 728 |

Ellipses | p. 737 |

Hyperbolas | p. 750 |

Plane Curves and Parametric Equations | p. 762 |

Polar Coordinates | p. 772 |

Polar Equations of Conics | p. 786 |

Chapter 11 Review Exercises | p. 792 |

Chapter 11 Discussion Exercises | p. 794 |

Appendixes | p. 797 |

Common Graphs and Their Equations | p. 798 |

A Summary of Graph Transformations | p. 800 |

Graphs of Trigonometric Functions and Their Inverses | p. 802 |

Values of the Trigonometric Functions of Special Angles on a Unit Circle | p. 804 |

Answers to Selected Exercises | p. A1 |

Index of Applications | p. A79 |

Index | p. A84 |

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