Precalculus: Concepts Through Functions, A Right Triangle Approach to Trigonometry

Cover
Title Page
Copyright Page
Contents
To the Student
Three Distinct Series
The Concepts through Functions Series
Preface to the Instructor
Applications Index
F. Foundations: A Prelude to Functions
	F.1. The Distance and Midpoint Formulas
	F.2. Graphs of Equations in Two Variables; Intercepts; Symmetry
	F.3. Lines
	F.4. Circles
	Chapter Project
1. Functions and Their Graphs
	1.1. Functions
	1.2. The Graph of a Function
	1.3. Properties of Functions
	1.4. Library of Functions; Piecewise-defined Functions
	1.5. Graphing Techniques: Transformations
	1.6. Mathematical Models: Building Functions
	1.7. Building Mathematical Models Using Variation
	Chapter Review
	Chapter Test
	Chapter Projects
2. Linear and Quadratic Functions
	2.1. Properties of Linear Functions and Linear Models
	2.2. Building Linear Models from Data
	2.3. Quadratic Functions and Their Zeros
	2.4. Properties of Quadratic Functions
	2.5. Inequalities Involving Quadratic Functions
	2.6. Building Quadratic Models from Verbal Descriptions and from Data
	2.7. Complex Zeros of a Quadratic Function
	2.8. Equations and Inequalities Involving the Absolute Value Function
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
3. Polynomial and Rational Functions
	3.1. Polynomial Functions and Models
	3.2. The Real Zeros of a Polynomial Function
	3.3. Complex Zeros; Fundamental Theorem of Algebra
	3.4. Properties of Rational Functions
	3.5. The Graph of a Rational Function
	3.6. Polynomial and Rational Inequalities
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
4. Exponential and Logarithmic Functions
	4.1. Composite Functions
	4.2. One-to-One Functions; Inverse Functions
	4.3. Exponential Functions
	4.4. Logarithmic Functions
	4.5. Properties of Logarithms
	4.6. Logarithmic and Exponential Equations
	4.7. Financial Models
	4.8. Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models
	4.9. Building Exponential, Logarithmic, and Logistic Models from Data
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
5. Trigonometric Functions
	5.1. Angles and Their Measure
	5.2. Right Triangle Trigonometry
	5.3. Computing the Values of Trigonometric Functions of Acute Angles
	5.4. Trigonometric Functions of any Angle
	5.5. Unit Circle Approach; Properties of the Trigonometric Functions
	5.6. Graphs of the Sine and Cosine Functions
	5.7. Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
	5.8. Phase Shift; Sinusoidal Curve Fitting
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
6. Analytic Trigonometry
	6.1. The Inverse Sine, Cosine, and Tangent Functions
	6.2. The Inverse Trigonometric Functions (Continued)
	6.3. Trigonometric Equations
	6.4. Trigonometric Identities
	6.5. Sum and Difference Formulas
	6.6. Double-angle and Half-angle Formulas
	6.7. Product-to-Sum and Sum-to-Product Formulas
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
7. Applications of Trigonometric Functions
	7.1. Applications Involving Right Triangles
	7.2. The Law of Sines
	7.3. The Law of Cosines
	7.4. Area of a Triangle
	7.5. Simple Harmonic Motion; Damped Motion; Combining Waves
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
8. Polar Coordinates; Vectors
	8.1. Polar Coordinates
	8.2. Polar Equations and Graphs
	8.3. The Complex Plane; De Moivre’s Theorem
	8.4. Vectors
	8.5. The Dot Product
	8.6. Vectors in Space
	8.7. The Cross Product
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
9. Analytic Geometry
	9.1. Conics
	9.2. The Parabola
	9.3. The Ellipse
	9.4. The Hyperbola
	9.5. Rotation of Axes; General Form of a Conic
	9.6. Polar Equations of Conics
	9.7. Plane Curves and Parametric Equations
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
10. Systems of Equations and Inequalities
	10.1. Systems of Linear Equations: Substitution and Elimination
	10.2. Systems of Linear Equations: Matrices
	10.3. Systems of Linear Equations: Determinants
	10.4. Matrix Algebra
	10.5. Partial Fraction Decomposition
	10.6. Systems of Nonlinear Equations
	10.7. Systems of Inequalities
	10.8. Linear Programming
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
11. Sequences; Induction; the Binomial Theorem
	11.1. Sequences
	11.2. Arithmetic Sequences
	11.3. Geometric Sequences; Geometric Series
	11.4. Mathematical Induction
	11.5. The Binomial Theorem
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
12. Counting and Probability
	12.1. Counting
	12.2. Permutations and Combinations
	12.3. Probability
	Chapter Review
	Chapter Test
	Cumulative Review
	Chapter Projects
13. A Preview of Calculus: The Limit, Derivative, and Integral of a Function
	13.1. Finding Limits Using Tables and Graphs
	13.2. Algebra Techniques for Finding Limits
	13.3. One-sided Limits; Continuous Functions
	13.4. The Tangent Problem; The Derivative
	13.5. The Area Problem; The Integral
	Chapter Review
	Chapter Test
	Chapter Projects
A. Review
	A.1. Algebra Essentials
	A.2. Geometry Essentials
	A.3. Polynomials
	A.4. Factoring Polynomials
	A.5. Synthetic Division
	A.6. Rational Expressions
	A.7. nth Roots; Rational Exponents
	A.8. Solving Equations
	A.9. Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications
	A.10. Interval Notation; Solving Inequalities
	A.11. Complex Numbers
B. Graphing Utilities
	B.1. The Viewing Rectangle
	B.2. Using a Graphing Utility to Graph Equations
	B.3. Using a Graphing Utility to Locate Intercepts and Check for Symmetry
	B.4. Using a Graphing Utility to Solve Equations
	B.5. Square Screens
	B.6. Using a Graphing Utility to Graph Inequalities
	B.7. Using a Graphing Utility to Solve Systems of Linear Equations
	B.8. Using a Graphing Utility to Graph a Polar Equation
	B.9. Using a Graphing Utility to Graph Parametric Equations
Answers
Subject Index
Photo Credits
Conics
Library of Functions
Formulas/Equations
Geometry Formulas
Trignometric Functions
Trignometric Identities
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