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# Study Guide for Stewart/Redlin/Watson's Algebra and Trigonometry, 3rd

**by**Stewart, James; Redlin, Lothar; Watson, Saleem

3rd

### 9781111568108

1111568103

Paperback

2/8/2011

Cengage Learning

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## Summary

This carefully crafted learning resource helps students develop their problem-solving skills while reinforcing their understanding with detailed explanations, worked-out examples, and practice problems. Students will also find listings of key ideas to master. Each section of the main text has a corresponding section in the Study Guide.

## Table of Contents

Prerequisites | p. 1 |

Real Numbers and Their Properties | p. 1 |

The Real Number Line and Order | p. 5 |

Integer Exponents | p. 8 |

Rational Exponents and Radicals | p. 11 |

Algebraic Expressions | p. 13 |

Factoring | p. 16 |

Rational Expressions | p. 22 |

Chapter P Word Search | p. 28 |

Equations and inequalities | p. 29 |

Basic Equations | p. 29 |

Modeling with Equations | p. 33 |

Quadratic Equations | p. 39 |

Complex Numbers | p. 43 |

Other Types of Equations | p. 46 |

Inequalities | p. 50 |

Absolute Value Equations and Inequalities | p. 55 |

Chapter 1 Word Search | p. 58 |

Coordinates and graphs | p. 59 |

The Coordinate Plane | p. 59 |

Graphs of Equations in Two Variables | p. 62 |

Graphing Calculators: Solving Equations and Inequalities Graphically | p. 66 |

Lines | p. 73 |

Making Models Using Variation | p. 80 |

Chapter 2 Word Search | p. 82 |

Functions | p. 83 |

What is a Function? | p. 83 |

Graphs of Functions | p. 85 |

Getting Information from the Graph of a Function | p. 89 |

Average Rate of Change of a Function | p. 93 |

Transformations of Functions | p. 95 |

Combining Functions | p. 103 |

One-to-One Functions and Their Inverses | p. 106 |

Chapter 3 Word Search | p. 112 |

Polynomial and rational functions | p. 113 |

Quadratic Functions and Models | p. 113 |

Polynomial Functions and TheirGraphs | p. 117 |

Dividing Polynomials | p. 123 |

Real Zeros of Polynomials | p. 126 |

Complex Zeros and the Fundamental Theorem of Algebra | p. 131 |

Rational Functions | p. 135 |

Chapter 4 WordSearch | p. 140 |

Exponential and logarithmic functions | p. 141 |

Exponential Functions | p. 141 |

The Natural Exponential Function | p. 143 |

Logarithmic Functions | p. 146 |

Laws of Logarithms | p. 149 |

Exponential and Logarithmic Equations | p. 152 |

Modeling with Exponential and Logarithmic Functions | p. 155 |

Chapter 5 Word Search | p. 159 |

Trigonometric functions: right triangle approach | p. 161 |

Angle Measure | p. 161 |

Trigonometry of Right Triangles | p. 164 |

Trigonometric Functions of Angles | p. 168 |

Inverse Trigonometric Functions and Triangles | p. 172 |

TheLaw of Sines | p. 175 |

The Law of Cosines | p. 177 |

Chapter 6 Word Search | p. 180 |

Trigonometric functions: unit circle approach | p. 181 |

The Unit Circle | p. 181 |

Trigonometric Functions of Real Numbers | p. 184 |

Trigonometric Graphs | p. 187 |

More Trigonometric Graphs | p. 191 |

Inverse Trigonometric Functions and TheirGraphs | p. 193 |

Modeling Harmonic Motion | p. 194 |

Chapter 7 Word Search | p. 197 |

Analytic trigonometry | p. 199 |

Trigonometric Identities | p. 199 |

Addition and Subtraction Formulas | p. 202 |

Double-Angle, Half-Angle, and Product-Sum Formulas | p. 204 |

Basic Trigonometric Equations | p. 208 |

More Trigonometric Equations | p. 210 |

Chapter 8 Word Search | p. 214 |

Polar Coordinates and Parametric Equations | p. 215 |

Polar Coordinates | p. 215 |

Graphs of Polar Equations | p. 218 |

Polar Form of Complex Numbers; De Moivre's Theorem | p. 222 |

PlaneCurvesand Parametric Equations | p. 227 |

Chapter 9 Word Search | p. 230 |

Vector in Two and Three Dimensions | p. 231 |

Vectors in Two Dimensions | p. 231 |

The Dot Product | p. 236 |

Three-Dimensional Coordinate Geometry | p. 240 |

Vectors in Three Dimensions | p. 242 |

The Cross Product | p. 244 |

Equations of Lines and Planes | p. 246 |

Chapter 10 Word Search | p. 248 |

System of Equations and Inequalities | p. 249 |

Systems of Linear Equations in Two Variables | p. 249 |

Systems of Linear Equations in Several Variables | p. 253 |

Matrices and Systems of Linear Equations | p. 257 |

The Algebra of Matrices | p. 263 |

Inverses of Matrices and Matrix Equations | p. 267 |

Determinants and Cramer's Rule | p. 273 |

Partial Fractions | p. 277 |

Systems of Nonlinear Equations | p. 282 |

Systems of Inequalities | p. 285 |

Chapter 11 Word Search | p. 289 |

Conic Sections | p. 291 |

Parabolas | p. 291 |

Ellipses | p. 294 |

Hyperbolas | p. 298 |

Shifted Conics | p. 301 |

Rotation of Axes | p. 305 |

PoSar Equations of Conies | p. 308 |

Chapter 12 Word Search | p. 312 |

Sequences and series | p. 313 |

Sequences and Summation Notation | p. 313 |

Arithmetic Sequences | p. 318 |

Geometric Sequences | p. 319 |

Mathematics of Finance | p. 322 |

Mathematical Induction | p. 324 |

The Binomial Theorem | p. 326 |

Chapter 13 Word Search | p. 329 |

Counting and probability | p. 331 |

Counting Principles | p. 331 |

Permutations and Combinations | p. 333 |

Probability | p. 337 |

Binomial Probability | p. 342 |

Expected Value | p. 344 |

Chapter 14 Word Search | p. 346 |

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