Algebra and Trigonometry: A Graphing Approach

by Larson, Ron

• ISBN13: 9780618052875
• ISBN10: 0618052879
• Edition: 3rd
• Format: Paperback
• Copyright: 2000-08-02
• Publisher: Brooks Cole

Summary

As part of the market-leading Graphing Approach series by Larson, Hostetler, and Edwards, Algebra and Trigonometry: A Graphing Approach, 4/e, provides both students and instructors with a sound mathematics course in an approachable, understandable format. The quality and quantity of the exercises, combined with interesting applications, cutting-edge design, and innovative resources, make teaching easier and help students succeed in mathematics. This edition, intended for algebra and trigonometry courses that require the use of a graphing calculator, includes a moderate review of algebra to help students entering the course with weak algebra skills.

Table of Contents

A word from the Authors (Preface)	vii
Features Highlights	xi
An Introduction to Graphing Utilities	xvii
Prerequisites	1	(66)
Real Numbers	2	(10)
Exponents and Radicals	12	(12)
Polynomials and Factoring	24	(13)
Rational Expressions	37	(10)
Graphical Representation of Data	47	(20)
Chapter Summary	59	(1)
Review Exercises	60	(4)
Chapter Project: Modeling the Volume of a Box	64	(1)
Chapter Test	65	(1)
Library of Functions	66	(1)
Functions and Their Graphs	67	(88)
Graphs of Equations	68	(11)
Lines in the Plane	79	(13)
Functions	92	(14)
Graphs of Functions	106	(12)
Shifting, Reflecting, and Stretching Graphs	118	(9)
Combinations of Functions	127	(11)
Inverse Functions	138	(17)
Chapter Summary	148	(1)
Review Exercises	149	(4)
Chapter Project: Modeling the Area of a Plot	153	(1)
Chapter Test	154	(1)
Intercepts, Zeros, and Solutions	155	(70)
Modeling with Linear Equations	156	(13)
Solving Equations Graphically	169	(11)
Complex Numbers	180	(8)
Solving Equations Algebraically	188	(17)
Solving Inequalities Algebraically and Graphically	205	(20)
Chapter Summary	217	(1)
Review Exercises	218	(3)
Chapter Project: Mozart and the Golden Ratio	221	(1)
Chapter Test	222	(1)
Cumulative Test: Chapter P--2	223	(2)
Polynomial and Rational Functions	225	(72)
Quadratic Functions	226	(11)
Polynomial Functions of Higher Degree	237	(13)
Real Zeros of Polynomial Functions	250	(14)
The Fundamental Theorem of Algebra	264	(7)
Rational Functions and Asymptotes	271	(10)
Graphs of Rational Functions	281	(16)
Chapter Summary	290	(1)
Review Exercises	291	(4)
Chapter Project: Finding Points of Intersection	295	(1)
Chapter Test	296	(1)
Exponential and Logarithmic Functions	297	(68)
Exponential Functions and Their Graphs	298	(13)
Logarithmic Functions and Their Graphs	311	(11)
Properties of Logarithms	322	(7)
Solving Exponential and Logarithmic Equations	329	(11)
Exponential and Logarithmic Models	340	(25)
Chapter Summary	356	(1)
Review Exercises	357	(4)
Chapter Project: A Graphical Approach to Compound Interest	361	(1)
Chapter Test	362	(1)
Cumulative Test: Chapters 3-4	363	(2)
Trigonometric Functions	365	(88)
Angles and Their Measure	366	(11)
Right Triangle Trigonometry	377	(11)
Trigonometric Functions of Any Angle	388	(13)
Graphs of Sine and Cosine Functions	401	(11)
Graphs of Other Trigonometric Functions	412	(11)
Inverse Trigonometric Functions	423	(10)
Applications and Models	433	(20)
Chapter Summary	445	(1)
Review Exercises	446	(5)
Chapter Project: Fitting a Model to Data	451	(1)
Chapter Test	452	(1)
Analytic Trigonometry	453	(52)
Using Fundamental Identities	454	(8)
Verifying Trigonometric Identities	462	(8)
Solving Trigonometric Equations	470	(12)
Sum and Difference Formulas	482	(7)
Multiple-Angle and Product-Sum Formulas	489	(16)
Chapter Summary	499	(1)
Review Exercises	500	(3)
Chapter Project: Projectile Motion	503	(1)
Chapter Test	504	(1)
Additional Topics in Trigonometry	505	(60)
Law of Sines	506	(9)
Law of Cosines	515	(7)
Vectors in the Plane	522	(14)
Vectors and Dot Products	536	(9)
Trigonometric Form of a Complex Number	545	(20)
Chapter Summary	556	(1)
Review Exercises	557	(4)
Chapter Project: Adding Vectors Graphically	561	(1)
Chapter Test	562	(1)
Cumulative Test: Chapters 5-7	563	(2)
Systems of Equations and Inequalities	565	(64)
Solving Systems of Equations	566	(11)
Systems of Linear Equations in Two Variables	577	(10)
Multivariable Linear Systems	587	(16)
Systems of Inequalities	603	(10)
Linear Programming	613	(16)
Chapter Summary	623	(1)
Review Exercises	624	(3)
Chapter Project: Fitting Models to Data	627	(1)
Chapter Test	628	(1)
Matrices and Determinats	629	(66)
Matrices and Systems of Equations	630	(15)
Operations with Matrices	645	(15)
The Inverse of a Square Matrix	660	(9)
The Determinant of a Square Matrix	669	(8)
Applications of Matrices and Determinants	677	(18)
Chapter Summary	687	(1)
Review Exercises	688	(5)
Chapter Project: Solving Systems of Equations	693	(1)
Chapter Test	694	(1)
Sequences, Series, and Probability	695	(78)
Sequences and Series	696	(11)
Arithmetic Sequences and Partial Sums	707	(9)
Geometric Sequences and Series	716	(10)
Mathematical Induction	726	(8)
The Binomial Theorem	734	(8)
Counting Principles	742	(10)
Probability	752	(21)
Chapter Summary	765	(1)
Review Exercises	766	(5)
Chapter Project: Fitting Models to Data	771	(1)
Chapter Test	772	(1)
Topics in Analytic Geometry	773
Conics	774
Translations of Conics	788
Parametric Equations	797
Polar Coordinates	805
Graphs of Polar Equations	811
Polar Equations of Conics	820
Chapter Summary	826
Review Exercises	827
Chapter Project: Polar, Rectangular, and Parametric Forms	831
Chapter Test	832
Cumulative Test: Chapters 8--11	833
Appendices
Appendix A Proofs of Selected Theorems	A1
Appendix B Concepts in Statistics	A14
B.1 Representing Data	A14
B.2 Measures of Central Tendency and Dispersion	A18
B.3 Least Squares Regression	A27
Appendix C Solving Linear Equations and Inequalities	A29
Answers to Odd-Numbered Exercises and Tests	A35
Index of Applications	A173
Index	A177