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9780131874756

Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry

by ;
  • ISBN13:

    9780131874756

  • ISBN10:

    0131874756

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2011-01-01
  • Publisher: Prentice Hall
  • View Upgraded Edition
  • Purchase Benefits
List Price: $176.00

Summary

This new text embodies Sullivan/Sullivanrs"s hallmarks accuracy, precision, depth, strong student support, and abundant exerciseswhile exposing students early (Chapter One) to the study of functionsand taking a unit circle approachto trigonometry."IT WORKS"for instructors and students because it focuses students on thefundamentals:preparingfor class,practicingtheir homework, andreviewing. After completing the book, students will be prepared to handle the algebra found in subsequent courses such as finite mathematics, business mathematics, and engineering calculus and will have a solid understanding of the concept of a function.

Table of Contents

Preface to the Instructor xiii
List of Applications
xix
Photo Credits xxiii
To the Student xxiv
Foundations: A Prelude To Functions
1(38)
The Distance and Midpoint Formulas
2(6)
Graphs of Equations in Two Variables; Intercepts; Symmetry
8(10)
Lines
18(15)
Circles
33(6)
Functions and Their Graphs
39(74)
Functions
40(14)
The Graph of a Function
54(9)
Properties of Functions
63(12)
Library of Functions; Piecewise-defined Functions
75(10)
Graphing Techniques: Transformations
85(12)
Mathematical Models: Constructing Functions
97(16)
Chapter Review
105(6)
Chapter Test
111(1)
Chapter Projects
112(1)
Linear and Quadratic Functions
113(68)
Properties of Linear Functions
114(11)
Building Linear Functions from Data; Direct Variation
125(8)
Quadratic Functions and Their Zeros
133(11)
Properties of Quadratic Functions
144(10)
Inequalities Involving Quadratic Functions
154(4)
Quadratic Models
158(9)
Complex Zeros of a Quadratic Function
167(3)
Equations and Inequalities Involving the Absolute Value Function
170(11)
Chapter Review
175(4)
Chapter Test
179(1)
Chapter Projects
179(1)
Cumulative Review
180(1)
Polynomial and Rational Functions
181(82)
Polynomial Functions and Models
182(21)
Properties of Rational Functions
203(10)
The Graph of a Rational Function; Inverse and Joint Variation
213(18)
Polynomial and Rational Inequalities
231(5)
The Real Zeros of a Polynomial Function
236(14)
Complex Zeros; Fundamental Theorem of Algebra
250(13)
Chapter Review
256(3)
Chapter Test
259(1)
Chapter Projects
260(1)
Cumulative Review
261(2)
Exponential and Logarithmic Functions
263(98)
Composite Functions
264(7)
One-to-One Functions; Inverse Functions
271(13)
Exponential Functions
284(16)
Logarithmic Functions
300(12)
Properties of Logarithms
312(8)
Logarithmic and Exponential Equations
320(5)
Compound Interest
325(9)
Exponential Growth and Decay; Newton's Law; Logistic Growth and Decay
334(11)
Building Exponential, Logarithmic, and Logistic Functions from Data
345(16)
Chapter Review
353(6)
Chapter Test
359(1)
Chapter Projects
359(1)
Cumulative Review
360(1)
Trigonometric Functions
361(84)
Angles and Their Measure
362(13)
Trigonometric Functions: Unit Circle Approach
375(15)
Properties of the Trigonometric Functions
390(14)
Graphs of the Sine and Cosine Functions
404(15)
Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
419(6)
Phase Shift; Sinusoidal Curve Fitting
425(20)
Chapter Review
436(6)
Chapter Test
442(1)
Chapter Projects
443(1)
Cumulative Review
443(2)
Analytic Trigonometry
445(68)
The Inverse Sine, Cosine, and Tangent Functions
446(12)
The Inverse Trigonometric Functions (Continued)
458(5)
Trigonometric Identities
463(8)
Sum and Difference Formulas
471(9)
Double-angle and Half-angle Formulas
480(9)
Product-to-Sum and Sum-to-Product Formulas
489(4)
Trigonometric Equations (I)
493(6)
Trigonometric Equations (II)
499(14)
Chapter Review
506(4)
Chapter Test
510(1)
Chapter Projects
510(1)
Cumulative Review
511(2)
Applications of Trigonometric Functions
513(52)
Right Triangle Trigonometry; Applications
514(12)
The Law of Sines
526(11)
The Law of Cosines
537(6)
Area of a Triangle
543(5)
Simple Harmonic Motion; Damped Motion; Combining Waves
548(17)
Chapter Review
557(4)
Chapter Test
561(1)
Chapter Projects
562(2)
Cumulative Review
564(1)
Polar Coordinates; Vectors
565(74)
Polar Coordinates
566(8)
Polar Equations and Graphs
574(16)
The Complex Plane; De Moivre's Theorem
590(8)
Vectors
598(11)
The Dot Product
609(8)
Vectors in Space
617(9)
The Cross Product
626(13)
Chapter Review
632(4)
Chapter Test
636(1)
Chapter Projects
637(1)
Cumulative Review
638(1)
Analytic Geometry
639(64)
Conics
640(1)
The Parabola
641(9)
The Ellipse
650(10)
The Hyperbola
660(12)
Rotation of Axes; General Form of a Conic
672(8)
Polar Equations of Conics
680(6)
Plane Curves and Parametric Equations
686(17)
Chapter Review
698(3)
Chapter Test
701(1)
Chapter Projects
701(1)
Cumulative Review
702(1)
Systems of Equations and Inequalities
703(96)
Systems of Linear Equations: Substitution and Elimination
704(14)
Systems of Linear Equations: Matrices
718(15)
Systems of Linear Equations: Determinants
733(10)
Matrix Algebra
743(16)
Partial Fraction Decomposition
759(7)
Systems of Nonlinear Equations
766(9)
Systems of Inequalities
775(8)
Linear Programming
783(16)
Chapter Review
790(5)
Chapter Test
795(1)
Chapter Projects
796(1)
Cumulative Review
797(2)
Sequences; Induction; The Binomial Theorem
799(40)
Sequences
800(9)
Arithmetic Sequences
809(5)
Geometric Sequences; Geometric Series
814(11)
Mathematical Induction
825(3)
The Binomial Theorem
828(11)
Chapter Review
835(2)
Chapter Test
837(1)
Chapter Projects
838(1)
Cumulative Review
838(1)
Counting and Probability
839(32)
Sets and Counting
840(5)
Permutations and Combinations
845(10)
Probability
855(16)
Chapter Review
865(3)
Chapter Test
868(1)
Chapter Projects
869(1)
Cumulative Review
869(2)
A Preview of Calculus: The Limit, Derivative, and Integral of a Function
871
Finding Limits Using Tables and Graphs
872(5)
Algebra Techniques for Finding Limits
877(7)
One-sided Limits; Continuous Functions
884(7)
The Tangent Problem; The Derivative
891(8)
The Area Problem; The Integral
899
Chapter Review
905(4)
Chapter Test
909(1)
Chapter Projects
910
Appendix A Review
1(1)
Algebra Essentials
1(10)
Geometry Essentials
11(8)
Polynomials
19(10)
Factoring Polynomials
29(9)
Synthetic Division
38(3)
Rational Expressions
41(11)
nth Roots; Rational Exponents
52(8)
Solving Equations
60(6)
Interval Notation; Solving Inequalities
66(8)
Problem Solving: Applications of Linear Equations
74(8)
Complex Numbers
82
Appendix B Graphing Utilities
1(1)
The Viewing Rectangle
1(2)
Using a Graphing Utility to Graph Equations
3(4)
Using a Graphing Utility to Locate Intercepts and Check for Symmetry
7(2)
Using a Graphing Utility to Solve Equations
9(2)
Square Screens
11(1)
Using a Graphing Utility to Graph Inequalities
12(2)
Using a Graphing Utility to Solve Systems of Linear Equations
14(1)
Using a Graphing Utility to Graph a Polar Equation
15(1)
Using a Graphing Utility to Graph Parametric Equations
16
Answers 1(1)
Index 1

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