Algebra and Trigonometry

by Larson, Ron; Hostetler, Robert P.

• ISBN13: 9780669417463
• ISBN10: 0669417467
• Edition: 4th
• Format: Hardcover
• Copyright: 1996-09-10
• Publisher: Brooks Cole

Table of Contents

Prerequisites	1	(80)
Real Numbers	2	(11)
Exponents and Radicals	13	(14)
Polynomials and Special Products	27	(9)
Factoring	36	(9)
Fractional Expressions	45	(11)
Errors and the Algebra of Calculus	56	(8)
Graphical Representation of Data	64	(17)
Focus on Concepts	74	(1)
Review Exercises	75	(3)
Chapter Project: A Numerical Approach to Maximizing a Volume	78	(2)
Chapter Test	80	(1)
Equations and Inequalities	81	(100)
Graphs and Graphing Utilities	82	(14)
Linear Equations	96	(10)
Modeling with Linear Equations	106	(13)
Quadratic Equations and Applications	119	(14)
Complex Numbers	133	(8)
Other Types of Equations	141	(12)
Linear Inequalities	153	(11)
Other Types of Inequalities	164	(17)
Focus on Concepts	174	(1)
Review Exercises	175	(3)
Chapter Project: A Numerical Approach to Finding Falling Times	178	(2)
Chapter Test	180	(1)
Functions and Their Graphs	181	(74)
Lines in the Plane and Slope	182	(15)
Functions	197	(14)
Analyzing Graphs of Functions	211	(12)
Translations and Combinations	223	(14)
Inverse Functions	237	(18)
Focus on Concepts	248	(1)
Review Exercises	249	(3)
Chapter Project: A Graphical Approach to Maximization	252	(2)
Cumulative Test for Chapters P--2	254	(1)
Zeros of Polynomial Functions	255	(78)
Quadratic Functions	256	(12)
Polynomial Functions of Higher Degree	268	(13)
Polynomial and Synthetic Division	281	(11)
Real Zeros of Polynomial Functions	292	(10)
The Fundamental Theorem of Algebra	302	(9)
Mathematical Modeling	311	(22)
Focus on Concepts	325	(1)
Review Exercises	326	(4)
Chapter Project: A Graphical Approach to Finding Zeros	330	(2)
Chapter Test	332	(1)
Rational Functions and Conics	333	(60)
Rational Functions and Asymptotes	334	(9)
Graphs of Rational Functions	343	(10)
Partial Fractions	353	(8)
Conics	361	(14)
Translations of Conics	375	(18)
Focus on Concepts	385	(1)
Review Exercises	386	(4)
Chapter Project: A Graphical Approach to Finding Average Cost	390	(2)
Chapter Test	392	(1)
Exponential and Logarithmic Functions	393	(62)
Exponential Functions and Their Graphs	394	(12)
Logarithmic Functions and Their Graphs	406	(11)
Properties of Logarithms	417	(7)
Exponential and Logarithmic Equations	424	(11)
Exponential and Logarithmic Models	435	(20)
Focus on Concepts	448	(1)
Review Exercises	449	(3)
Chapter Project: A Graphical Approach to Compound Interest	452	(2)
Cumulative Test for Chapters 3--5	454	(1)
Trigonometry	455	(92)
Angles and Their Measure	456	(11)
Right Triangle Trigonometry	467	(12)
Trigonometric Functions of Any Angle	479	(13)
Graphs of Sine and Cosine Functions	492	(13)
Graphs of Other Trigonometric Functions	505	(12)
Inverse Trigonometric Functions	517	(11)
Applications and Models	528	(19)
Focus on Concepts	540	(1)
Review Exercises	541	(3)
Chapter Project: Analyzing a Graph	544	(2)
Chapter Test	546	(1)
Analytic Trigonometry	547	(54)
Using Fundamental Identities	548	(8)
Verifying Trigonometric Identities	556	(8)
Solving Trigonometric Equations	564	(11)
Sum and Difference Formulas	575	(8)
Multiple-Angle and Product-to-Sum Formulas	583	(18)
Focus on Concepts	595	(1)
Review Exercises	596	(2)
Chapter Project: Solving Equations Graphically	598	(2)
Chapter Test	600	(1)
Additional Topics in Trigonometry	601	(62)
Law of Sines	602	(10)
Law of Cosines	612	(9)
Vectors in a Plane	621	(14)
Vectors and Dot Products	635	(10)
DeMoivre's Theorem	645	(18)
Focus on Concepts	656	(1)
Review Exercises	657	(3)
Chapter Project: Adding Vectors Graphically	660	(2)
Cumulative Test for Chapter 6--8	662	(1)
Systems of Equations and Inequalities	663	(66)
Solving Systems of Equations	664	(11)
Two-Variable Linear Systems	675	(12)
Multivariable Linear Systems	687	(13)
Systems of Inequalities	700	(10)
Linear Programming	710	(19)
Focus on Concepts	721	(1)
Review Exercises	722	(4)
Chapter Project: Fitting Models to Data	726	(2)
Chapter Test	728	(1)
Matrices and Determinants	729	(68)
Matrices and Systems of Equations	730	(15)
Operations with Matrices	745	(14)
The Inverse of a Square Matrix	759	(10)
The Determinant of a Square Matrix	769	(9)
Applications of Matrices and Determinants	778	(19)
Focus on Concepts	790	(1)
Review Exercises	791	(3)
Chapter Project: Solving Systems of Equations	794	(2)
Chapter Test	796	(1)
Sequences and Probability	797
Sequences and Summation Notation	798	(12)
Arithmetic Sequences	810	(9)
Geometric Sequences	819	(10)
Mathematical Induction	829	(11)
The Binomial Theorem	840	(8)
Counting Principles	848	(10)
Probability	858
Focus on Concepts	872	(1)
Review Exercises	873	(3)
Chapter Project: Recognizing Patterns in Data	876	(2)
Cumulative Test for Chapters 9--11	878
APPENDICES	A1
Appendix A: Further Concepts in Statistics	A2
A.1 Representing Data and Linear Modeling	A2
A.2 Measures of Central Tendency and Dispersion	A13
Appendix B: Think About the Proof	A21
Appendix C: Programs	A31
Appendix D: Scientific Calculator Keystrokes	A69
Answers to Warm UPS, Odd-Numbered Exercises, Focus on Concepts, and Tests	A73
Index of Applications	A193
Index	A199