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Tables of Contents for Algebra and Trigonometry With Analytic Geometry
Chapter/Section Title
Page #
Page Count
Preface
vii
 
Fundamental Concepts of Algebra
1
52
Real Numbers
2
14
Exponents and Radicals
16
11
Algebraic Expressions
27
13
Fractional Expressions
40
13
Review Exercises
50
2
Discussion Exercises
52
1
Equations and Inequalities
53
72
Equations
54
8
Applied Problems
62
12
Quadratic Equations
74
14
Complex Numbers
88
6
Other Types of Equations
94
9
Inequalities
103
9
More on Inequalities
112
13
Review Exercises
120
3
Discussion Exercises
123
2
Functions and Graphs
125
106
Rectangular Coordinate Systems
126
6
Graphs of Equations
132
10
Lines
142
15
Definition of Function
157
16
Graphs of Functions
173
12
Quadratic Functions
185
11
Operations on Functions
196
9
Inverse Functions
205
11
Variation
216
15
Review Exercises
222
6
Discussion Exercises
228
3
Polynomial and Rational functions
231
54
Polynomial Functions of Degree Greater Than 2
232
8
Properties of Division
240
8
Zeros of Polynomials
248
10
Complex and Rational Zeros of Polynomials
258
7
Rational Functions
265
20
Review Exercises
282
2
Discussion Exercises
284
1
Exponential and Logarithmic functions
285
60
Exponential Functions
286
10
The Natural Exponential Function
296
8
Logarithmic Functions
304
16
Properties of Logarithms
320
8
Exponential and Logarithmic Equations
328
17
Review Exercises
340
3
Discussion Exercises
343
2
The Trigonometric functions
345
94
Angles
346
10
Trigonometric Functions of Angles
356
17
Trigonometric Functions of Real Numbers
373
18
Values of the Trigonometric Functions
391
8
Trigonometric Graphs
399
12
Additional Trigonometric Graphs
411
8
Applied Problems
419
20
Review Exercises
431
7
Discussion Exercises
438
1
Analytic Trigonometry
439
64
Verifying Trigonometric Identities
440
5
Trigonometric Equations
445
12
The Addition and Subtraction Formulas
457
11
Multiple-Angle Formulas
468
10
Product-to-Sum and Sum-to-Product Formulas
478
5
The Inverse Trigonometric Functions
483
20
Review Exercises
498
3
Discussion Exercises
501
2
Applications of Trigonometry
503
60
The Law of Sines
504
10
The Law of Cosines
514
9
Vectors
523
14
The Dot Product
537
10
Trigonometric Form for Complex Numbers
547
6
De Moivre's Theorem and nth Roots of Complex Numbers
553
10
Review Exercises
558
4
Discussion Exercises
562
1
Systems of Equations and Inequalities
563
90
Systems of Equations
564
9
Systems of Linear Equations in Two Variables
573
9
Systems of Inequalities
582
8
Linear Programming
590
9
Systems of Linear Equations in More Than Two Variables
599
14
The Algebra of Matrices
613
9
The Inverse of a Matrix
622
6
Determinants
628
6
Properties of Determinants
634
8
Partial Fractions
642
11
Review Exercises
648
3
Discussion Exercises
651
2
Sequences, Series, and Probability
653
78
Infinite Sequences and Summation Notation
654
10
Arithmetic Sequences
664
7
Geometric Sequences
671
9
Mathematical Induction
680
7
The Binomial Theorem
687
9
Permutations
696
7
Distinguishable Permutations and Combinations
703
9
Probability
712
19
Review Exercises
725
3
Discussion Exercises
728
3
Topics from Analytic Geometry
731
70
Parabolas
732
9
Ellipses
741
13
Hyperbolas
754
12
Plane Curves and Parametric Equations
766
11
Polar Coordinates
777
13
Polar Equations of Conics
790
11
Review Exercises
796
2
Discussion Exercises
798
3
Appendixes
801
1
I Common Graphs and Their Equations
802
2
II A Summary of Graph Transformations
804
2
III Graphs of Trigonometric Functions and Their Inverses
806
2
IV Values of the Trigonometric Functions of Special Angles on a Unit Circle
808
 
Answers to Selected Exercises
A1
 
Index of Applications
A75
 
Index
A80