جبر و مثلثات

Cover Page......Page 1 Chapter Review Features......Page 2 To the Student......Page 3 Dedication Page......Page 5 Title Page......Page 8 Copyright Page......Page 9 CONTENTS......Page 10 Three Distinct Series......Page 16 Preface to the Instructor......Page 17 Student Resources......Page 22 Applications Index......Page 24 Photo Credits......Page 31 R: Review......Page 34 R.1 Real Numbers......Page 35 R.2 Algebra Essentials......Page 50 R.3 Geometry Essentials......Page 63 R.4 Polynomials......Page 72 R.5 Factoring Polynomials......Page 82 R.6 Synthetic Division......Page 91 R.7 Rational Expressions......Page 95 R.8 nth Roots; Rational Exponents......Page 106 1 Equations and Inequalities......Page 114 1.1 Linear Functions......Page 115 1.2 Quadratic Equations......Page 125 1.3 Complex Numbers; Quadratic Equations in the Complex Number System......Page 137 1.4 Radical Equations;Equations Quadratic in Form; Factorable Equations......Page 146 1.5 Solving Inequalities......Page 152 1.6 Equations and Inequalities Involving Absolute Value......Page 163 1.7 Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications......Page 167 Chapter Review......Page 176 Chapter Test......Page 180 Chapter Projects......Page 181 2 Graphs......Page 182 2.1 The Distance and Midpoint Formulas......Page 183 2.2 Graphs of Equations in Two Variables; Intercepts; Symmetry......Page 190 2.3 Lines......Page 200 2.4 Circles......Page 215 2.5 Variation......Page 221 Chapter Review......Page 227 Chapter Project......Page 230 3 Functions and Their Graphs......Page 232 3.1 Functions......Page 233 3.2 The Graph of a Function......Page 247 3.3 Properties of Functions......Page 255 3.4 Library of Functions; Piecewise-defined Functions......Page 267 3.5 Graphing Techniques:Transformations......Page 277 3.6 Mathematical Models: Building Functions......Page 290 Chapter Review......Page 296 Chapter Test......Page 301 Chapter Projects......Page 302 4 Linear and Quadratic Functions......Page 304 4.1 Linear Functions and Their Properties......Page 305 4.2 Linear Models: Building Linear Functions from Data......Page 315 4.3 Quadratic Functions and Their Properties......Page 321 4.4 Build Quadratic Models from Verbal Descriptions and from Data......Page 333 4.5 Inequalities Involving Quadratic Functions......Page 342 Chapter Review......Page 346 Chapter Test......Page 349 Cumulative Review......Page 350 Chapter Projects......Page 351 5 Polynomial and Rational Functions......Page 352 5.1 Polynomial Functions and Models......Page 353 5.2 Properties of Rational Functions......Page 375 5.3 The Graph of a Rational Function......Page 386 5.4 Polynomial and Rational Inequalities......Page 401 5.5 The Real Zeros of a Polynomial Function......Page 407 5.6 Complex Zeros; Fundamental Theorem of Algebra......Page 420 Chapter Review......Page 426 Cumulative Review......Page 430 Chapter Projects......Page 431 6 Exponential and Logarithmic Functions......Page 433 6.1 Composite Functions......Page 434 6.2 One-to-One Functions; Inverse Functions......Page 441 6.3 Exponential Functions......Page 454 6.4 Logarithmic Functions......Page 470 6.5 Properties of Logarithms......Page 483 6.6 Logarithmic and Exponential Equations......Page 492 6.7 Financial Models......Page 499 6.8 Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models......Page 509 6.9 Building Exponential, Logarithmic, and Logistic Models from Data......Page 519 Chapter Review......Page 527 Cumulative Review......Page 533 Chapter Projects......Page 534 7 Trigonometric Functions......Page 536 7.1 Angles and Their Measure......Page 537 7.2 Right Triangle Trigonometry......Page 550 7.3 Computing the Values of Trigonometric Functions of Acute Angles......Page 562 7.4 Trigonometric Functions of Any Angle......Page 573 7.5 Unit Circle Approach; Properties of the Trigonometric Functions......Page 583 7.6 Graphs of the Sine and Cosine Functions......Page 594 7.7 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions......Page 609 7.8 Phase Shift; Sinusoidal Curve Fitting......Page 616 Chapter Review......Page 627 Chapter Test......Page 633 Cumulative Review......Page 634 Chapter Projects......Page 635 8 Analytic Trigonometry......Page 636 8.1 The Inverse Sine, Cosine, and Tangent Functions......Page 637 8.2 The Inverse Trigonometric Functions (Continued)......Page 649 8.3 Trigonometric Equations......Page 655 8.4 Trigonometric Identities......Page 665 8.5 Sum and Difference Formulas......Page 673 8.6 Double-angle and Half-angle Formulas......Page 685 8.7 Product-to-Sum and Sum-to-Product Formulas......Page 695 Chapter Review......Page 699 Cumulative Review......Page 703 Chapter Projects......Page 704 9 Applications of Trigonometric Functions......Page 705 9.1 Applications Involving Right Triangles......Page 706 9.2 The Law of Sines......Page 711 9.3 The Law of Cosines......Page 722 9.4 Area of a Triangle......Page 729 9.5 Simple Harmonic Motion; Damped Motion; Combining Waves......Page 735 Chapter Review......Page 744 Chapter Test......Page 747 Cumulative Review......Page 748 Chapter Projects......Page 749 10 Polar Coordinates;Vectors......Page 750 10.1 Polar Coordinates......Page 751 10.2 Polar Equations and Graphs......Page 760 10.3 The Complex Plane; De Moivre’s Theorem......Page 775 10.4 Vectors......Page 782 10.5 The Dot Product......Page 796 Chapter Review......Page 803 Chapter Test......Page 806 Chapter Projects......Page 807 11 Analytic Geometry......Page 809 11.1 Conics......Page 810 11.2 The Parabola......Page 811 11.3 The Ellipse......Page 820 11.4 The Hyperbola......Page 830 11.5 Rotation of Axes; General Form of a Conic......Page 843 11.6 Polar Equations of Conics......Page 851 11.7 Plane Curves and Parametric Equations......Page 856 Chapter Review......Page 869 Chapter Test......Page 872 Chapter Projects......Page 873 12 Systems of Equations and Inequalities......Page 875 12.1 Systems of Linear Equations: Substitution and Elimination......Page 876 12.2 Systems of Linear Equations: Matrices......Page 891 12.3 Systems of Linear Equations: Determinants......Page 906 12.4 Matrix Algebra......Page 915 12.5 Partial Fraction Decomposition......Page 932 12.6 Systems of Nonlinear Equations......Page 940 12.7 Systems of Inequalities......Page 949 12.8 Linear Programming......Page 956 Chapter Review......Page 963 Chapter Test......Page 968 Chapter Projects......Page 969 13 Sequences; Induction; the Binomial Theorem......Page 971 13.1 Sequences......Page 972 13.2 Arithmetic Sequences......Page 982 13.3 Geometric Sequences; Geometric Series......Page 988 13.4 Mathematical Induction......Page 999 13.5 The Binomial Theorem......Page 1003 Chapter Review......Page 1009 Cumulative Review......Page 1012 Chapter Projects......Page 1013 14 Counting and Probability......Page 1014 14.1 Counting......Page 1015 14.2 Permutations and Combinations......Page 1020 14.3 Probability......Page 1029 Chapter Review......Page 1039 Chapter Test......Page 1041 Chapter Projects......Page 1042 1 The Viewing Rectangle......Page 1044 2 Using a Graphing Utility to Graph Equations......Page 1046 3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry......Page 1048 4 Using a Graphing Utility to Solve Equations......Page 1049 5 Square Screens......Page 1051 7 Using a Graphing Utility to Solve Systems of Linear Equations......Page 1052 9 Using a Graphing Utility to Graph Parametric Equations......Page 1054 Answers......Page 1056 INDEX......Page 1150 Prepare for Class.........Page 1170 Practice.........Page 1171 Info Sheets......Page 1172