Algebra and Trigonometry : Graphing, Data, and Analysis

by Sullivan, Michael; Sullivan, Michael

• ISBN13: 9780131404533
• ISBN10: 0131404539
• Edition: 2nd
• Format: Hardcover
• Copyright: 2004-01-01
• Publisher: Pearson College Div

Table of Contents

Preface to the Instructor	xiii
Preface to the Student	xviii
Photo and Illustration Credits	xix
List of Applications	xxviii
Equations, Inequalities, and Functions	1	(88)
Solving Equations and Inequalities in One Variable Algebraically	2	(14)
Rectangular Coordinates; Graphing Utilities	16	(9)
Introduction to Graphing Equations	25	(8)
Symmetry; Graphing Key Equations; Circles	33	(13)
Solving Equations and Inequalities in One Variable Using a Graphing Utility	46	(5)
Introduction to Functions	51	(13)
The Graph of a Function	64	(8)
Properties of Functions	72	(17)
Chapter Review	82	(5)
Chapter Projects	87	(2)
Linear Functions and Models	89	(54)
Properties of Linear Functions	90	(13)
Equations of Lines; Building Linear Functions	103	(13)
Setting Up Linear Equations; Applications	116	(13)
Building Linear Functions from Data	129	(14)
Chapter Review	137	(4)
Chapter Projects	141	(1)
Cumulative Review	142	(1)
Quadratic Functions and Models	143	(54)
Quadratic Equations	144	(13)
The Graph of a Quadratic Function	157	(13)
Inequalities Involving Quadratic Functions	170	(5)
Quadratic Models: Building Quadratic Functions	175	(7)
Complex Numbers; Quadratic Equations with a Negative Discriminant	182	(15)
Chapter Review	191	(3)
Chapter Projects	194	(1)
Cumulative Review	195	(2)
Additional Functions and Models	197	(46)
Radical Equations; Absolute Value Equations; Absolute Value Inequalities	198	(9)
Library of Functions; Piecewise-defined Functions	207	(11)
Graphing Techniques: Transformations	218	(13)
Models Involving the Square Root Function and Piecewise-defined Functions	231	(12)
Chapter Review	238	(2)
Chapter Projects	240	(1)
Cumulative Review	241	(2)
Polynomial and Rational Functions	243	(80)
Power Functions and Models	244	(6)
Polynomial Functions and Models	250	(15)
Rational Functions I	265	(12)
Rational Functions II: Analyzing Graphs	277	(13)
Polynomial and Rational Inequalities	290	(6)
The Real Zeros of a Polynomial Function	296	(14)
Complex Zeros; Fundamental Theorem of Algebra	310	(13)
Chapter Review	316	(4)
Chapter Projects	320	(2)
Cumulative Review	322	(1)
Exponential and Logarithmic Functions	323	(106)
Composite Functions	324	(7)
Inverse Functions	331	(14)
Exponential Functions	345	(16)
Logarithmic Functions	361	(12)
Properties of Logarithms	373	(9)
Logarithmic and Exponential Equations	382	(5)
Compound Interest	387	(10)
Exponential Growth and Decay	397	(8)
Logistic Growth and Decay	405	(6)
Fitting Data to Exponential, Logarithmic and Logistic Functions	411	(18)
Chapter Review	419	(7)
Chapter Projects	426	(1)
Cumulative Review	427	(2)
Trigonometric Functions	429	(88)
Angles and Their Measure	430	(14)
Trigonometric Functions: Unit Circle Approach	444	(16)
Properties of the Trigonometric Functions	460	(15)
Graphs of the Sine and Cosine Functions	475	(16)
Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions	491	(6)
Phase Shifts; Sinusoidal Curve Fitting	497	(20)
Chapter Review	508	(6)
Chapter Projects	514	(1)
Cumulative Review	515	(2)
Analytic Trigonometry	517	(70)
The Inverse Sine, Cosine, and Tangent Functions	518	(12)
The Inverse Trigonometric Functions (continued)	530	(5)
Trigonometric Identities	535	(8)
Sum and Difference Formulas	543	(10)
Double-Angle and Half-Angle Formulas	553	(10)
Product-to-Sum and Sum-to-Product Formulas	563	(3)
Trigonometric Equations (I)	566	(7)
Trigonometric Equations (II)	573	(14)
Chapter Review	580	(4)
Chapter Projects	584	(1)
Cumulative Review	585	(2)
Applications of Trigonometric Functions	587	(54)
Right Triangle Trigonometry	588	(13)
The Law of Sines	601	(11)
The Law of Cosines	612	(6)
Area of a Triangle	618	(6)
Simple Harmonic Motion; Damped Motion; Combining Waves	624	(17)
Chapter Review	634	(4)
Chapter Projects	638	(2)
Cumulative Review	640	(1)
Polar Coordinates; Vectors	641	(80)
Polar Coordinates	642	(9)
Polar Equations and Graphs	651	(18)
The Complex Plane; De Moivre's Theorem	669	(9)
Vectors	678	(12)
The Dot Product	690	(8)
Vectors in Space	698	(10)
The Cross Product	708	(13)
Chapter Review	715	(4)
Chapter Projects	719	(1)
Cumulative Review	720	(1)
Analytic Geometry	721	(78)
Conics	722	(1)
The Parabola	723	(11)
The Ellipse	734	(13)
The Hyperbola	747	(15)
Rotation of Axes; General Form of a Conic	762	(9)
Polar Equations of Conics	771	(7)
Plane Curves and Parametric Equations	778	(21)
Chapter Review	793	(4)
Chapter Projects	797	(1)
Cumulative Review	798	(1)
Systems of Equations and Inequalities	799	(106)
Systems of Linear Equations: Substitution and Elimination	800	(15)
Systems of Linear Equations: Matrices	815	(17)
Systems of Linear Equations: Determinants	832	(12)
Matrix Algebra	844	(18)
Partial Fraction Decomposition	862	(7)
Systems of Nonlinear Equations	869	(12)
Systems of Inequalities	881	(9)
Linear Programming	890	(15)
Chapter Review	898	(5)
Chapter Projects	903	(1)
Cumulative Review	904	(1)
Sequences; Induction; the Binomial Theorem	905	(50)
Sequences	906	(15)
Arithmetic Sequences	921	(6)
Geometric Sequences; Geometric Series	927	(10)
Mathematical Induction	937	(4)
The Binomial Theorem	941	(14)
Chapter Review	949	(3)
Chapter Projects	952	(2)
Cumulative Review	954	(1)
Counting and Probability	955	(44)
Sets and Counting	956	(6)
Permutations and Combinations	962	(11)
Probability of Equally Likely Outcomes	973	(14)
Obtaining Probabilities from Data	987	(12)
Chapter Review	993	(4)
Chapter Projects	997	(1)
Cumulative Review	998	(1)
A Preview of Calculus: The Limit, Derivative, and Integral of a Function	999
Finding Limits Using Tables and Graphs	1000	(5)
Algebra Techniques for Finding Limits	1005	(7)
One-sided Limits; Continuous Functions	1012	(7)
The Tangent Problem; the Derivative	1019	(9)
The Area Problem; the Integral	1028
Chapter Review	1036	(3)
Chapter Projects	1039
REVIEW	1	(1)
Algebra Review	1	(10)
Geometry Review	11	(5)
Polynomials	16	(12)
Rational Expressions	28	(9)
Polynomial Division; Synthetic Division	37	(6)
nth Roots; Rational Exponents	43
Answers	1	(1)
Index	1