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Tables of Contents for Precalculus With Unit-Circle Trigonometry
Chapter/Section Title
Page #
Page Count
1 ALGEBRA BACKGROUND FOR PRECALCULUS
1
34
1.1 Sets of Real Numbers
1
5
1.2 Absolute Value
6
5
1.3 Polynomials and Factoring
11
9
1.4 Quadratic Equations
20
15
2 COORDINATES, GRAPHS, AND INEQUALITIES
35
66
2.1 Rectangular Coordinates
35
12
2.2 Graphs and Equations, a Second Look
47
10
2.3 Equations of Lines
57
12
2.4 Symmetry and Graphs
69
8
2.5 Inequalities
77
8
2.6 More on Inequalities
85
16
3 FUNCTIONS
101
74
3.1 The Definition of a Function
101
12
3.2 The Graph of a Function
113
17
3.3 Techniques in Graphing
130
12
3.4 Methods of Combining Functions. Iteration
142
12
3.5 Inverse Functions
154
21
4 POLYNOMIAL AND RATIONAL FUNCTIONS. APPLICATIONS TO ITERATION AND OPTIMIZATION
175
95
4.1 Linear Functions
175
14
4.2 Quadratic Functions
189
9
4.3 More on Iteration. Quadratics and Population Growth
198
17
4.4 Applied Functions: Setting Up Equations
215
12
4.5 Maximum and Minimum Problems
227
11
4.6 Polynomial Functions
238
13
4.7 Rational Functions
251
19
5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
270
87
5.1 Exponential Functions
271
9
5.2 The Exponential Function y = e(x)
280
9
5.3 Logarithmic Functions
289
12
5.4 Properties of Logarithms
301
9
5.5 Equations and Inequalities with Logs and Exponents
310
11
5.6 Compound Interest
321
11
5.7 Exponential Growth and Decay
332
25
6 THE TRIGONOMETRIC FUNCTIONS
357
59
6.1 Radian Measure
357
14
6.2 Trigonometric Functions of Angles
371
11
6.3 Evaluating the Trigonometric Functions
382
8
6.4 Algebra and the Trigonometric Functions
390
10
6.5 Right-Triangle Trigonometry
400
16
7 GRAPHS OF THE TRIGONOMETRIC FUNCTIONS
416
62
7.1 Trigonometric Functions of Real Numbers
417
11
7.2 Graphs of the Sine and Cosine Functions
428
16
7.3 Graphs of y = A sin(Bx - C) and y = A cos(Bx - C)
444
12
7.4 Simple Harmonic Motion
456
6
7.5 Graphs of the Tangent and the Reciprocal Functions
462
16
8 ANALYTICAL TRIGONOMETRY
478
59
8.1 The Addition Formulas
478
9
8.2 The Double-Angle Formulas
487
10
8.3 Product-to-Sum and Sum-to-Product Formulas
497
5
8.4 Trigonometric Equations
502
14
8.5 The Inverse Trigonometric Functions
516
21
9 ADDITIONAL TOPICS IN TRIGONOMETRY
537
79
9.1 Right-Triangle Applications
537
14
9.2 The Law of Sines and the Law of Cosines
551
16
9.3 Vectors in the Plane, a Geometric Approach
567
7
9.4 Vectors in the Plane, an Algebraic Approach
574
8
9.5 Parametric Equations
582
12
9.6 Introduction to Polar Coordinates
594
5
9.7 Graphs in Polar Coordinates
599
17
10 SYSTEMS OF EQUATIONS
616
72
10.1 Systems of Two Linear Equations in Two Unknowns
616
11
10.2 Gaussian Elimination
627
8
10.3 Matrices
635
12
10.4 The Inverse of a Square Matrix
647
7
10.5 Determinants and Cramer's Rule
654
13
10.6 Nonlinear Systems of Equations
667
7
10.7 Systems of Inequalities
674
14
11 ANALYTIC GEOMETRY
688
80
11.1 The Basic Equations
688
9
11.2 The Parabola
697
11
11.3 Tangents to Parabolas (Optional)
708
3
11.4 The Ellipse
711
15
11.5 The Hyperbola
726
11
11.6 The Focus-Directrix Property of Conics
737
9
11.7 The Conics in Polar Coordinates
746
6
11.8 Rotation of Axes
752
16
12 ROOTS OF POLYNOMIAL EQUATIONS
768
70
12.1 The Complex Number System
768
8
12.2 Division of Polynomials
776
7
12.3 Roots of Polynomial Equations: The Remainder Theorem and the Factor Theorem
783
8
12.4 The Fundamental Theorem of Algebra
791
9
12.5 Rational and Irrational Roots
800
8
12.6 Conjugate Roots and Descartes's Rule of Signs
808
6
12.7 Introduction to Partial Fractions
814
7
12.8 More About Partial Fractions
821
17
13 ADDITIONAL TOPICS
838
 
13.1 Mathematical Induction
838
6
13.2 The Binomial Theorem
844
10
13.3 Introduction to Sequences and Series
854
7
13.4 Arithmetic Sequences and Series
861
5
13.5 Geometric Sequences and Series
866
5
13.6 DeMoivre's Theorem
871
 
APPENDIXES
A-1
28
A.1 Using a Graphing Utility
A-3
4
A.2 Significant Digits and Calculators
A-7
4
A.3 Properties of the Real Numbers
A-11
7
A.4 XXX2 Is Irrational
A-18
1
A.5 Review of Integer Exponents and nth Roots
A-19
7
A.6 Review of Rational Exponents
A-26
3
TABLES
A-29
12
1 Exponential Functions
A-30
1
2 Logarithms to the Base Ten
A-31
2
3 Natural Logarithms
A-33
1
4 Values of Trigonometric Functions
A-34
7
ANSWERS TO SELECTED EXERCISES
A-41
 
INDEX
I-1