Anyone trying to learn algebra and trigonometry may think they understand a concept but then are unable to apply that understanding when they attempt to complete exercises. This innovative book helps them overcome common barriers to learning the concepts and builds confidence in their ability to do mathematics. The second edition presents new sections on modeling at the end of each chapter as well as new material on Limits and Early Functions. Numerous examples are also included that provide more detailed annotations using everyday language. This approach gives them the skills to understand and apply algebra and trigonometry.
CHAPTER 0 PREREQUISITES AND REVIEW
0.1 Real Numbers
0.2 Integer Exponents and Scientific Notation
0.3 Polynomials: Basic Operations
0.4 Factoring Polynomials
0.5 Rational Expressions
0.6 Rational Exponents and Radicals
0.7 Complex Numbers
Modeling Your World
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Review Exercises
Practice Test
Cumulative Test
CHAPTER 1 EQUATIONS AND INEQUALITIES
1.1 Linear Equations
1.2 Applications Involving Linear Equations
1.3 Quadratic Equations
1.4 Other Types of Equations
1.5 Linear Inequalities
1.6 Polynomial and Rational Inequalities
1.7 Absolute Value Equations and Inequalities
Modeling Your World
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CHAPTER 2 GRAPHS
2.1 Basic Tools: Cartesian Plane, Distance, and Midpoint
2.2 Graphing Equations: Point-Plotting, Intercepts and Symmetry
2.3 Lines
2.4 Circles
Modeling Your World
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Review Exercises
Practice Test
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CHAPTER 3 FUNCTIONS AND THEIR GRAPHS
3.1 Functions
3.2 Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change
3.3 Graphing Techniques: Transformations
3.4 Operation on Functions and Composition of Functions
3.5 One-to-One Functions and Inverse Functions
3.6 Modeling Functions Using Variation
Modeling Your World
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CHAPTER 4 POLYNOMIAL AND RATIONAL FUNCTIONS
4.1 Quadratic Functions
4.2 Polynomial Functions of Higher Degree
4.3 Dividing Polynomials: Long Division and Synthetic Division
4.4 The Real Zeros of a Polynomial Function
4.5 Complex Zeros; The Fundamental Theorem of Algebra
4.6 Rational Functions
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CHAPTER 5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
5.1 Exponential Functions and Their Graphs
5.2 Exponential Functions and Their Graphs
5.3 Properties of Logarithms
5.4 Exponential and Logarithmic Equations
5.5 Exponential and Logarithmic Models
Modeling Your World
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Practice Test
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CHAPTER 6 TRIGONOMETRIC FUNCTIONS
6.1 Angles, Degrees and Triangles
6.2 Definition 1 of Trigonometric Functions: Right Triangle Ratios
6.3 Applications of Right Triangle Trigonometry: Solving Right Triangles
6.4 Definition 2 of Trigonometric Functions: Cartesian Plane
6.5 Trigonometric Functions of Non-Acute Angles
6.6 Radian Measure and Applications
6.7 Definition 3 of Trigonometric Functions: Unit Circle Approach
6.8 Graphs of Sine and Cosine Functions
6.9 Graphs of Other Trigonometric Functions
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CHAPTER 7 ANALYTIC TRIGONOMETRY
7.1 Basic Trigonometric Identities
7.2 Verifying Trigonometric Identities
7.3 Sum and Difference Identities
7.4 Double-Angle Identities
7.5 Half-Angle Identities
7.6 Product-to-Sum and Sum-to-Product Identities
7.7 Inverse Trigonometric Functions
7.8 Trigonometric Equations
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CHAPTER 8 ADDITIONAL TOPIC IN TRIGONOMETRY
8.1 Oblique Triangles and The Law of Sines
8.2 The Law of Cosines
8.3 Area of a Triangle
8.4 Vectors
8.5 Dot Product
8.6 Polar (Trigonometric) Form of Complex Numbers
8.7 Products, Quotients, Powers and Roots of Complex Numbers
8.8 Polar Equations and Graphs
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CHAPTER 9 SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES
9.1 Systems of Linear Equations in Two Variables
9.2 Systems of Linear Equations in Three Variables
9.3 Partial Fractions
9.4 Systems of Linear Inequalities in Two Variables
9.5 The Linear Programming Model
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CHAPTER 10 MATRICES
10.1 Matrices and Systems of Linear Equations
10.2 Matrix Algebra
10.3 Matrix Equations; The Inverse of a Square Matrix
10.4 The Determinant of a Square Matrix and Cramer's Rule
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CHAPTER 11 ANALYTIC GEOMETRY
11.1 Conic Basics
11.2 The Parabola
11.3 The Ellipse
11.4 The Hyperbola
11.5 Systems of Nonlinear Equations
11.6 Systems of Nonlinear Inequalities
11.7 Rotation of Axes
11.8 Polar Equations of Conics
11.9 Parametric Equations and Graphs
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CHAPTER 12 SEQUENCES, SERIES, AND PROBABILITY
12.1 Sequences and Series
12.2 Arithmetic Sequences and Series
12.3 Geometric Sequences and Series
12.4 Mathematical Induction
12.5 Binomial Theorem
12.6 Counting, Permutations, and Combinations
12.7 Probability
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