Algebra & Trigonometry

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