Precalculus / Edition 7

Precalculus / Edition 7

by Michael Sullivan
     
 

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ISBN-10: 0131913999

ISBN-13: 9780131913998

Pub. Date: 03/12/2004

Publisher: Pearson

This book motivates through realistic applications to people of diverse mathematical backgrounds. Develops the trigonometric functions using a unit circle approach and progresses to the right triangle approach. Graphing techniques are emphasized, including a thorough discussion of polar coordinates, parametric equations, and conics using polar coordinates.

Overview

This book motivates through realistic applications to people of diverse mathematical backgrounds. Develops the trigonometric functions using a unit circle approach and progresses to the right triangle approach. Graphing techniques are emphasized, including a thorough discussion of polar coordinates, parametric equations, and conics using polar coordinates.

Product Details

ISBN-13:
9780131913998
Publisher:
Pearson
Publication date:
03/12/2004
Edition description:
New Edition
Pages:
1001

Table of Contents


Preface to the Instructor     xiii
List of Applications     xix
Photo Credits     xxv
To the Student     xxvi
Graphs     1
The Distance and Midpoint Formulas     2
Graphs of Equations in Two Variables; Intercepts; Symmetry     9
Lines     19
Circles     35
Chapter Review     42
Chapter Test     44
Chapter Projects     45
Functions and Their Graphs     47
Functions     48
The Graph of a Function     62
Properties of Functions     71
Library of Functions; Piecewise-defined Functions     82
Graphing Techniques: Transformations     92
Mathematical Models: Building Functions     104
Chapter Review     109
Chapter Test     114
Cumulative Review     115
Chapter Projects     116
Linear and Quadratic Functions     117
Linear Functions and Their Properties     118
Building Linear Functions from Data     127
Quadratic Functions and Their Properties     133
Quadratic Models; Building Quadratic Functions from Data     145
Inequalities Involving Quadratic Functions     154
Chapter Review     158
Chapter Test     160
Cumulative Review     161
Chapter Projects     162
Polynomial and Rational Functions     163
Polynomial Functions and Models     164
Properties of Rational Functions     184
The Graph of a Rational Function     195
Polynomial and Rational Inequalities     209
The Real Zeros of a Polynomial Function     215
Complex Zeros; Fundamental Theorem of Algebra     229
Chapter Review     234
Chapter Test     238
Cumulative Review     238
Chapter Projects     239
Exponential and Logarithmic Functions     241
Composite Functions     242
One-to-One Functions; Inverse Functions     249
Exponential Functions     263
Logarithmic Functions     277
Properties of Logarithms     290
Logarithmic and Exponential Equations     299
Compound Interest     305
Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models     315
Building Exponential, Logarithmic, and Logistic Models from Data      327
Chapter Review     334
Chapter Test     340
Cumulative Review     341
Chapter Projects     342
Trigonometric Functions     343
Angles and Their Measure     344
Trigonometric Functions: Unit Circle Approach     357
Properties of the Trigonometric Functions     373
Graphs of the Sine and Cosine Functions     386
Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions     401
Phase Shift; Sinusoidal Curve Fitting     408
Chapter Review     419
Chapter Test     424
Cumulative Review     425
Chapter Projects     426
Analytic Trigonometry     427
The Inverse Sine, Cosine, and Tangent Functions     428
The Inverse Trigonometric Functions (Continued)     440
Trigonometric Identities     446
Sum and Difference Formulas     453
Double-angle and Half-angle Formulas     463
Product-to-Sum and Sum-to-Product Formulas     472
Trigonometric Equations (I)     475
Trigonometric Equations (II)     482
Chapter Review     489
Chapter Test     492
Cumulative Review      493
Chapter Projects     493
Applications of Trigonometric Functions     495
Applications Involving Right Triangles     496
The Law of Sines     508
The Law of Cosines     519
Area of a Triangle     525
Simple Harmonic Motion; Damped Motion; Combining Waves     531
Chapter Review     541
Chapter Test     545
Cumulative Review     546
Chapter Projects     546
Polar Coordinates; Vectors     549
Polar Coordinates     550
Polar Equations and Graphs     558
The Complex Plane; DeMoivre's Theorem     574
Vectors     582
The Dot Product     593
Vectors in Space     601
The Cross Product     610
Chapter Review     616
Chapter Test     620
Cumulative Review     620
Chapter Projects     621
Analytic Geometry     623
Conics     624
The Parabola     625
The Ellipse     634
The Hyperbola     644
Rotation of Axes; General Form of a Conic     656
Polar Equations of Conics      664
Plane Curves and Parametric Equations     670
Chapter Review     682
Chapter Test     685
Cumulative Review     685
Chapter Projects     686
Systems of Equations and Inequalities     687
Systems of Linear Equations: Substitution and Elimination     688
Systems of Linear Equations: Matrices     702
Systems of Linear Equations: Determinants     717
Matrix Algebra     727
Partial Fraction Decomposition     743
Systems of Nonlinear Equations     750
Systems of Inequalities     759
Linear Programming     767
Chapter Review     773
Chapter Test     777
Cumulative Review     778
Chapter Projects     779
Sequences; Induction; the Binomial Theorem     781
Sequences     782
Arithmetic Sequences     791
Geometric Sequences; Geometric Series     797
Mathematical Induction     809
The Binomial Theorem     813
Chapter Review     819
Chapter Test     822
Cumulative Review     822
Chapter Projects     823
Counting and Probability      825
Counting     826
Permutations and Combinations     831
Probability     840
Chapter Review     850
Chapter Test     852
Cumulative Review     853
Chapter Projects     853
A Preview of Calculus: The Limit, Derivative, and Integral of a Function     855
Finding Limits Using Tables and Graphs     856
Algebra Techniques for Finding Limits     861
One-sided Limits; Continuous Functions     868
The Tangent Problem; The Derivative     875
The Area Problem; The Integral     883
Chapter Review     889
Chapter Test     893
Chapter Projects     894
Review     A1
Algebra Essentials     A1
Geometry Essentials     A14
Polynomials     A22
Synthetic Division     A31
Rational Expressions     A35
Solving Equations     A43
Complex Numbers; Quadratic Equations in the Complex Number System     A54
Problem Solving: Interest, Mixture, Uniform Motion, Constant Rate Job Applications     A62
Interval Notation; Solving Inequalities     A72
nth Roots; Rational Exponents      A81
Graphing Utilities     B1
The Viewing Rectangle     B1
Using a Graphing Utility to Graph Equations     B3
Using a Graphing Utility to Locate Intercepts and Check for Symmetry     B6
Using a Graphing Utility to Solve Equations     B8
Square Screens     B10
Using a Graphing Utility to Graph Inequalities     B11
Using a Graphing Utility to Solve Systems of Linear Equations     B12
Using a Graphing Utility to Graph a Polar Equation     B13
Using a Graphing Utility to Graph Parametric Equations     B14
Answers     AN1
Index     I1

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