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Tables of Contents for Algebra and Trigonometry With Analytic Geometry
Chapter/Section Title
Page #
Page Count
List of Graphing Calculator Topics
ix
Preface
xi
Fundamental Concepts of Algebra
1
58
Real Numbers
2
17
19
12
Algebraic Expressions
31
14
Fractional Expressions
45
14
Review Exercises
56
2
Discussion Exercises
58
1
Equations and Inequalities
59
72
Equations
60
9
Applied Problems
69
11
80
14
Complex Numbers
94
7
Other Types of Equations
101
9
Inequalities
110
9
More on Inequalities
119
12
Review Exercises
127
3
Discussion Exercises
130
1
Functions and Graphs
131
130
Rectangular Coordinate Systems
132
9
Graphs of Equations
141
16
Lines
157
18
Definition of Function
175
18
Graphs of Functions
193
16
209
15
Operations on Functions
224
11
Inverse Functions
235
10
Variation
245
16
Review Exercises
252
6
Discussion Exercises
258
3
Polynomial and Rational Functions
261
64
Polynomial Functions of Degree Greater Than 2
262
11
Properties of Division
273
8
Zeros of Polynomials
281
14
Complex and Rational Zeros of Polynomials
295
8
Rational Functions
303
22
Review Exercises
321
2
Discussion Exercises
323
2
Exponential and Logarithmic Functions
325
66
Exponential Functions
326
12
The Natural Exponential Function
338
10
Logarithmic Functions
348
16
Properties of Logarithms
364
8
Exponential and Logarithmic Equations
372
19
Review Exercises
385
3
Discussion Exercises
388
3
The Trigonometric Functions
391
102
Angles
392
11
Trigonometric Functions of Angels
403
18
Trigonometric Functions of Real Numbers
421
19
Values of the Trigonometric Functions
440
8
Trigonometric Graphs
448
15
463
8
Applied Problems
471
22
Review Exercises
484
7
Discussion Exercises
491
2
Analytic Trigonometry
493
68
Verifying Trigonometric Identities
494
6
Trigonometric Equations
500
15
515
11
Multiple-Angle Formulas
526
10
Product-to-Sum and Sum-to-Product Formulas
536
5
The Inverse Trigonometric Functions
541
20
Review Exercises
557
3
Discussion Exercises
560
1
Applications of Trigonometry
561
64
The Law of Sines
562
10
The Law of Cosines
572
9
Vectors
581
15
The Dot Product
596
11
Trigonometric Form for Complex Numbers
607
7
De Moivre's Theorem and nth Roots of Complex Numbers
614
11
Review Exercises
620
4
Discussion Exercises
624
1
Systems of Equations and Inequalities
625
96
Systems of Equations
626
9
Systems of Linear Equations in Two Variables
635
9
Systems of Inequalities
644
9
Linear Programming
653
9
Systems of Linear Equations in More Than Two Variables
662
15
The Algebra of Matrices
677
10
The Inverse of a Matrix
687
7
Determinants
694
7
Properties of Determinants
701
8
Partial Fractions
709
12
Review Exercises
715
3
Discussion Exercises
718
3
Sequences, Series, and Probability
721
84
Infinite Sequences and Summation Notation
722
16
Arithmetic Sequences
738
7
Geometric Sequences
745
9
Mathematical Induction
754
7
The Binomial Theorem
761
9
Permutations
770
7
Distinguishable Permutations and Combinations
777
9
Probability
786
19
Review Exercises
799
3
Discussion Exercises
802
3
Topics from Analytic Geometry
805
78
Parabolas
806
10
Ellipses
816
14
Hyperbolas
830
12
Plane Curves and Parametric Equations
842
15
Polar Coordinates
857
16
Polar Equations of Conics
873
10
Review Exercises
879
2
Discussion Exercises
881
2
Appendixes
883
I Common Graphs and Their Equations
884
II A Summary of Graph Transformations
886
III Graphs of Trigonometric Functions and Their Inverses
888
IV Values of the Trigonometric Functions of Special Angles on a Unit Circle
890