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Algebra and Trigonometry, 8th Edition

Richard N. Aufmann, Richard D. Nation

  • Copyright 2015
  • {{checkPublicationMessage('Published', '2014-01-01T00:00:00+0000')}}
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Algebra and Trigonometry 8th Edition by Richard N. Aufmann/Richard D. Nation
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Overview

Accessible to students and flexible for instructors, COLLEGE ALGEBRA AND TRIGONOMETRY, Eighth Edition, incorporates the dynamic link between concepts and applications to bring mathematics to life. By integrating interactive learning techniques, the Aufmann author team helps students to better understand concepts, work independently, and obtain greater mathematical fluency. The text also includes technology features to accommodate courses that allow the option of using graphing calculators. The authors' proven Aufmann Interactive Method allows students to try a skill as it is presented in example form. This interaction between the examples and Try Exercises serves as a checkpoint to students as they read the textbook, do their homework, or study a section. In the eighth edition, Review Notes are featured more prominently throughout the text to help students recognize the key prerequisite skills needed to understand new concepts.

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Meet the Authors

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Richard N. Aufmann

Richard Aufmann is the lead author of two best-selling DEVELOPMENTAL MATH series and a best-selling COLLEGE ALGEBRA AND TRIGONOMETRY series, as well as several derivative math texts. Mr. Aufmann taught math, computer science and physics at Palomar College in California, where he was on the faculty for 28 years. His textbooks are highly recognized and respected among college mathematics professors. Today, Mr. Aufmann's professional interests include quantitative literacy, the developmental math curriculum and the impact of technology on curriculum development. He holds a Bachelor of Arts in Mathematics from the University of California, Irvine and a Master of Arts degree in Mathematics from California State University, Long Beach.

Richard D. Nation

Richard Nation received a B.A. in mathematics from Morningside College and a M.S. degree in mathematics from the University of South Dakota. Mr. Nation also attended a National Science Foundation academic year institute in mathematics at San Diego State University. Mr. Nation taught math at Palomar College in California, where he was on the faculty for 20 years. He has over 38 years’ experience teaching mathematics at the high school and college levels. He is the co-author of several Aufmann titles. Today, Mr. Nation’s professional interests include the impact of technology on curriculum development and on the teaching of mathematics at the precalculus level.

What's New

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  • NEW Concept Check Exercises--Each exercise set starts with exercises that are designed to test your students' understanding of new concepts.
  • NEW Enrichment Exercises--Each exercise set concludes with an exercise or exercises that are designed to extend the concepts presented in the section or to provide exercises that challenge your students' problem-solving abilities.
  • NEW Interactive Demonstrations--New Interactive Demonstrations allow you to adjust parameters and immediately see the change produced by your adjustment. These Interactive Demonstrations run on computers and on mobile devices. Instructions for using each of the demonstrations are provided. You can access these Interactive Demonstrations by scanning a QR code, with a QR reader app, or by using the web address supplied in the directions.
  • NEW An Interactive Technology Approach via WolframAlpha--Several Integrating Technology features show how WolframAlpha can be used to perform computations, solve equations, graph functions, and find regression functions. WolframAlpha runs on computers and mobile devices. WolframAlpha often provides an alternative to the use of a graphing calculator. WolframAlpha can be accessed by scanning a QR code or by using the address: http://www.wolframalpha.com.

Features

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  • Mid-Chapter Quizzes help you assess your students' understanding of the concepts studied earlier in the chapter. The answers for all exercises in the Mid-Chapter Quizzes are provided in the Answers to Selected Exercises appendix, along with a reference to the section in which a particular concept was presented.
  • Chapter Test Preps summarize the major concepts discussed in each chapter. These Test Preps help your students prepare for a chapter test. For each concept there is a reference to a worked example illustrating the concept and at least one exercise in the Chapter Review Exercise Set relating to that concept.
  • Visualize the Solution, available with both algebraic and graphical solutions when appropriate, are provided to help you visualize the mathematics of the example and to create a link between the algebraic and visual components of a solution.
  • "Exploring Concepts with Technology" feature appears after the last section in each chapter and provides you the option to use calculators or computers to solve computationally difficult problems. In addition, students are challenged to think about pitfalls that can be produced when using technology to solve mathematical problems.
  • "Integrating Technology" boxes show how technology can be used to illustrate concepts and solve many mathematical problems. Examples and exercises that require a calculator or a computer to find a solution are identified by the graphing calculator icon.
  • Modeling sections and exercises rely on the use of a graphing calculator or a computer. These optional sections and exercises introduce the idea of a mathematical model and help you see the relevance of mathematical concepts.
  • Chapter Review Exercise Sets and Chapter Tests at the end of each chapter are designed to provide you with another opportunity to assess your students' understanding of the concepts presented in a chapter. The answers for all exercises in the Chapter Review Exercise Sets and the Chapter Tests are provided in the Answers to Selected Exercises appendix, along with a reference to the section in which the concept was presented.

Table of Contents

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PRELIMINARY CONCEPTS.
The Real Number System. Integer and Rational Number Exponents. Polynomials. Mid-Chapter P Quiz. Factoring. Rational Expressions. Complex Numbers. Exploring Concepts with Technology. Chapter P Test Prep. Chapter P Review Exercises. Chapter P Test.
1. EQUATIONS AND INEQUALITIES.
Linear and Absolute Value Equations. Formulas and Applications. Quadratic Equations. Mid-Chapter 1 Quiz. Other Types of Equations. Inequalities. Variation and Applications. Exploring Concepts with Technology. Chapter 1 Test Prep. Chapter 1 Review Exercises. Chapter 1 Test. Cumulative Review Exercises.
2. FUNCTIONS AND GRAPHS.
Two-Dimensional Coordinate System and Graphs. Introduction to Functions. Linear Functions. Mid-Chapter 2 Quiz. Quadratic Functions. Properties of Graphs. Algebra of Functions. Modeling Data using Regression. Exploring Concepts with Technology. Chapter 2 Test Prep. Chapter 2 Review Exercises. Chapter 2 Test. Chapter 2 Cumulative Review Exercises.
3. POLYNOMIAL AND RATIONAL FUNCTIONS.
Remainder Theorem and Factor Theorem. Polynomial Functions of Higher Degree. Zeros of Polynomial Functions. Mid-Chapter 3 Quiz. Fundamental Theorem of Algebra. Graphs of Rational Functions and Their Applications. Exploring Concepts with Technology. Chapter 3 Test Prep. Chapter 3 Review Exercises. Chapter 3 Test. Cumulative Review Exercises.
4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Inverse Functions. Exponential Functions and Their Applications. Logarithmic Functions and Their Applications. Properties of Logarithms and Logarithmic Scales. Mid-Chapter 4 Quiz. Exponential and Logarithmic Equations. Exponential Growth and Decay. Modeling Data with Exponential and Logarithmic Functions. Exploring Concepts with Technology. Chapter 4 Test Prep. Chapter 4 Review Exercises. Chapter 4 Test. Cumulative Review Exercises.
5. TRIGONOMETRIC FUNCTIONS.
Angles and Arcs. Right Triangle Trigonometry. Trigonometric Functions of Any Angle. Trigonometric Functions of Real Numbers. Mid-Chapter 5 Quiz. Graphs of the Sine and Cosine Functions. Graphs of the Other Trigonometric Functions. Graphing Techniques. Harmonic Motion--An Application of the Sine and Cosine Functions. Exploring Concepts with Technology. Chapter 5 Test Prep. Chapter 5 Review Exercises. Chapter 5 Test. Cumulative Review Exercises.
6. TRIGONOMETRIC IDENTITIES AND EQUATIONS.
Verification of Trigonometric Identities. Sum, Difference, and Cofunction Identities. Double- and Half-Angle Identities. Mid-Chapter 6 Quiz. Identities Involving the Sum of Trigonometric Functions. Inverse Trigonometric Functions. Trigonometric Equations. Exploring Concepts with Technology. Chapter 6 Test Prep. Chapter 6 Review Exercises. Chapter 6 Test. Cumulative Review Exercises.
7. APPLICATIONS OF TRIGONOMETRY.
Law of Sines. Law of Cosines and Area. Vectors. Mid-Chapter 7 Quiz. Trigonometric Form of Complex Numbers. De Moivre's Theorem. Exploring Concepts with Technology. Chapter 7 Test Prep. Chapter 7 Review Exercises. Chapter 7 Test. Cumulative Review Exercises.
8. TOPICS IN ANALYTIC GEOMETRY.
Parabolas. Ellipses. Hyperbolas. Rotation of Axes. Mid-Chapter 8 Quiz. Introduction to Polar Coordinates. Polar Equations of the Conics. Parametric Equations of the Conics. Exploring Concepts with Technology. Chapter 8 Test Prep. Chapter 8 Review Exercises. Chapter 8 Test. Cumulative Review Exercises.
9. SYSTEMS OF EQUATIONS AND INEQUALITIES.
Systems of Linear Equations in Two Variables. Systems of Linear Equations in Three Variables. Nonlinear Systems of Equations. Mid-Chapter 9 Quiz. Partial Fractions. Inequalities in Two Variables and Systems of Inequalities. Linear Programming. Exploring Concepts with Technology. Chapter 9 Test Prep. Chapter 9 Review Exercises. Chapter 9 Test. Cumulative Review Exercises.
10. MATRICES.
Gaussian Elimination Method. Algebra of Matrices. Inverse of a Matrix. Mid-Chapter 10 Quiz. Determinants. Exploring Concepts with Technology. Chapter 10 Test Prep. Chapter 10 Review Exercises. Chapter 10 Test. Cumulative Review Exercises.
11. SEQUENCES, SERIES, AND PROBABILITY.
Infinite Sequences and Summation Notation. Arithmetic Sequences and Series. Geometric Sequences and Series. Mid-Chapter 11 Quiz. Mathematical Induction. Binomial Theorem. Permutations and Combinations. Introduction to Probability. Exploring Concepts with Technology. Chapter 11 Test Prep. Chapter 11 Review Exercises. Chapter 11 Test. Cumulative Review Exercises. Solutions to the Try Exercises.
Answers to Selected Exercises. Instructor Additional Answers.
Index.

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Supplements

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Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.

FOR INSTRUCTORS

Study Guide with Student Solutions Manual for Aufmann's Algebra and Trigonometry, 8th

ISBN: 9781285451121
Reinforces student understanding and aids in test preparation with detailed explanations, worked-out examples, and practice problems. Lists key ideas to master and builds problem-solving skills. Includes worked solutions to the odd-numbered problems in the text.

FOR STUDENTS

Study Guide with Student Solutions Manual for Aufmann's Algebra and Trigonometry, 8th

ISBN: 9781285451121
Reinforces student understanding and aids in test preparation with detailed explanations, worked-out examples, and practice problems. Lists key ideas to master and builds problem-solving skills. Includes worked solutions to the odd-numbered problems in the text.

WebAssign Instant Access for Aufmann/Nation's Algebra and Trigonometry, Multi-Term

ISBN: 9781337763790
WebAssign for Algebra and Trigonometry is a flexible and fully customizable online instructional solution that puts powerful tools in the hands of instructors, enabling you to deploy assignments, instantly assess individual student and class performance and help your students master the course concepts. Enrich the teaching and learning experience with the superior content within the powerful digital platform of WebAssign. Tailor your course with a wide range of assignment settings, the ability to add your own questions and content, analytics at the individual and course level and student/teacher communication tools.