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Tables of Contents for Algebra and Trigonometry With Analytic Geometry
Chapter/Section Title
Page #
Page Count
PREFACE
x
 
CHAPTER 1 FUNDAMENTAL CONCEPTS OF ALGEBRA
1
52
1.1 Real Numbers
2
13
1.2 Exponents and Radicals
15
12
1.3 Algebraic Expressions
27
13
1.4 Fractional Expressions
40
9
CHAPTER 1 REVIEW EXERCISES
49
2
CHAPTER 1 DISCUSSION EXERCISES
51
2
CHAPTER 2 EQUATIONS AND INEQUALITIES
53
70
2.1 Equations
54
8
2.2 Applied Problems
62
12
2.3 Quadratic Equations
74
12
2.4 Complex Numbers
86
6
2.5 Other Types of Equations
92
9
2.6 Inequalities
101
9
2.7 More on Inequalities
110
7
CHAPTER 2 REVIEW EXERCISES
117
3
CHAPTER 2 DISCUSSION EXERCISES
120
3
CHAPTER 3 FUNCTIONS AND GRAPHS
123
114
3.1 Rectangular Coordinate Systems
124
7
3.2 Graphs of Equations
131
13
3.3 Lines
144
17
3.4 Definition of Function
161
15
3.5 Graphs of Functions
176
13
3.6 Quadratic Functions
189
14
3.7 Operations on Functions
203
10
3.8 Inverse Functions
213
10
3.9 Variation
223
6
CHAPTER 3 REVIEW EXERCISES
229
5
CHAPTER 3 DISCUSSION EXERCISES
234
3
CHAPTER 4 POLYNOMIAL AND RATIONAL FUNCTIONS
237
56
4.1 Polynomial Functions of Degree Greater Than 2
238
8
4.2 Properties of Division
246
8
4.3 Zeros of Polynomials
254
13
4.4 Complex and Rational Zeros of Polynomials
267
8
4.5 Rational Functions
275
15
CHAPTER 4 REVIEW EXERCISES
290
2
CHAPTER 4 DISCUSSION EXERCISES
292
1
CHAPTER 5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
293
60
5.1 Exponential Functions
294
11
5.2 The Natural Exponential Function
305
10
5.3 Logarithmic Functions
315
15
5.4 Properties of Logarithms
330
8
5.5 Exponential and Logarithmic Equations
338
10
CHAPTER 5 REVIEW EXERCISES
348
2
CHAPTER 5 DISCUSSION EXERCISES
350
3
CHAPTER 6 THE TRIGONOMETRIC FUNCTIONS
353
96
6.1 Angles
354
9
6.2 Trigonometric Functions of Angles
363
16
6.2 Trigonometric Functions of Real Numbers
379
19
6.4 Values of the Trigonometric Functions
398
7
6.5 Trigonometric Graphs
405
15
6.6 Additional Trigonometric Graphs
420
9
6.7 Applied Problems
429
13
CHAPTER 6 REVIEW EXERCISES
442
6
CHAPTER 6 DISCUSSION EXERCISES
448
1
CHAPTER 7 ANALYTIC TRIGONOMETRY
449
64
7.1 Verifying Trigonometric Identities
450
5
7.2 Trigonometric Equations
455
12
7.3 The Addition and Subtraction Formulas
467
11
7.4 Multiple-Angle Formulas
478
10
7.5 Product-to-Sum and Sum-to-Product Formulas
488
5
7.6 The Inverse Trigonometric Functions
493
15
CHAPTER 7 REVIEW EXERCISES
508
3
CHAPTER 7 DISCUSSION EXERCISES
511
2
CHAPTER 8 APPLICATIONS OF TRIGONOMETRY
513
60
8.1 The Law of Sines
514
10
8.2 The Law of Cosines
524
10
8.3 Trigonometric Form for Complex Numbers
534
5
8.4 De Moivre's Theorem and nth Roots of Complex Numbers
539
5
8.5 Vectors
544
14
8.6 The Dot Product
558
10
CHAPTER 8 REVIEW EXERCISES
568
3
CHAPTER 8 DISCUSSION EXERCISES
571
2
CHAPTER 9 SYSTEMS OF EQUATIONS AND INEQUALITIES
573
90
9.1 Systems of Equations
574
9
9.2 Systems of Linear Equations in Two Variables
583
8
9.3 Systems of Linear Equations in More Than Two Variables
591
15
9.4 Partial Fractions
606
6
9.5 Systems of Inequalities
612
7
9.6 Linear Programming
619
9
9.7 The Algebra of Matrices
628
9
9.8 The Inverse of a Matrix
637
6
9.9 Determinants
643
7
9.10 Properties of Determinants
650
8
CHAPTER 9 REVIEW EXERCISES
658
3
CHAPTER 9 DISCUSSION EXERCISES
661
2
CHAPTER 10 SEQUENCES, SERIES, AND PROBABILITY
663
72
10.1 Infinite Sequences and Summation Notation
664
9
10.2 Arithmetic Sequences
673
7
10.3 Geometric Sequences
680
9
10.4 Mathematical Induction
689
6
10.5 The Binomial Theorem
695
9
10.6 Permutations
704
7
10.7 Distinguishable Permutations and Combinations
711
7
10.8 Probability
718
12
CHAPTER 10 REVIEW EXERCISES
730
3
CHAPTER 10 DISCUSSION EXERCISES
733
2
CHAPTER 11 TOPICS AND ANALYTIC GEOMETRY
735
69
11.1 Parabolas
736
10
11.2 Ellipses
746
13
11.3 Hyperbolas
759
13
11.4 Plane Curves and Parametric Equations
772
10
11.5 Polar Coordinates
782
12
11.6 Polar Equations of Conics
794
7
CHAPTER II REVIEW EXERCISES
801
2
CHAPTER II DISCUSSION EXERCISES
803
1
APPENDIXES
804
 
I Using a TI-82/83 Graphing Calculator
804
38
II Common Graphs and Their Equations
842
2
III A Summary of Graph Transformations
844
2
IV Graphs of Trigonometric Functions and Their Inverses
846
 
ANSWERS TO SELECTED EXERCISES
A1
88
INDEX OF APPLICATIONS
A89
6
INDEX
A95