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Algebra and Trigonometry: Real Mathematics, Real People 7th Edition

Ron Larson

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Overview

ALGEBRA AND TRIGONOMETRY: REAL MATHEMATICS, REAL PEOPLE, 7th Edition, is an ideal student and instructor resource for courses that require the use of a graphing calculator. Retaining the series' emphasis on student support, selected examples throughout include notations directing students to previous sections to review concepts and skills needed to master the material at hand. The edition also achieves accessibility through careful writing and design. Similarly, side-by-side solutions show algebraic, graphical, and numerical representations of the mathematics and support a variety of learning styles. Reflecting its subtitle, this revision focuses more than ever on showing students the relevance of mathematics in their lives.

Ron Larson, The Pennsylvania State University, The Behrend College

Dr. Ron Larson is a professor of mathematics at The Pennsylvania State University, where he has taught since 1970. He received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2014 William Holmes McGuffey Longevity Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, the 2013 Text and Academic Authors Association Award for CALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS (a complete text on CD-ROM that was the first mainstream college textbook to be offered on the Internet). Dr. Larson authors numerous textbooks including the bestselling Calculus series published by Cengage.

WebAssign is a flexible and fully customizable online instructional solution that puts powerful tools in the hands of teachers, enabling you to realize your teaching goals and instantly assess individual student performance to help students learn math, not just do online homework.

  • Side-By-Side Examples. Throughout the text, we present solutions to many examples from multiple perspectives-algebraically, graphically, and numerically. The side-by-side format of this pedagogical feature helps students to see a problem can be solved in more than one way and to see different methods yield the same result. The side-by-side format also addresses many different learning styles.
  • Why You Should Learn It Exercise. An engaging, real-life application of the concepts in the section, this application exercise is typically described in the section opener as a motivator for the section.
  • Library of Parent Functions. Several elementary and non-elementary functions have been compiled as a Library of Parent Functions to facilitate familiarity with the basic functions. Each function is introduced at the first point of use in the text with a definition and description of basic characteristics. The Library of Parent Functions examples are identified in the title of the example and there is a Review of Library of Parent Functions after Chapter 4. A summary of functions is presented on the inside cover of this text.
  • Make a Decision. The Make a Decision exercises at the end of selected sections involve in-depth applied exercises in which students work with large, real-life data sets, often creating or analyzing models. These exercises are offered online at LarsonPrecalculus.com.
  • Explore the Concept. Each Explore the Concept engages students in active discovery of mathematical concepts, strengthens critical thinking skills, and helps build intuition.
  • What's Wrong. Each What's Wrong points out common errors made using graphing utilities.
  • Technology Tip. Technology Tips provide graphing calculator tips or provide alternate methods of solving a problem using a graphing utility.
  • Algebra of Calculus. Throughout the text, special emphasis is given to the algebraic techniques used in calculus. Algebra of calculus examples and exercises are integrated throughout the text.
  • Algebraic-Graphical-Numerical Exercises. These exercises allow students to solve a problem using multiple approaches—algebraic, graphical, and numerical. This helps students to see that a problem can be solved in more than one way and to see that different methods yield the same result.
  • Modeling Data Exercises. These multi-part applications that involve real-life data offer students the opportunity to generate and analyze mathematical models.
  • Vocabulary and Concept Check. The Vocabulary and Concept Check appears at the beginning of the exercise set for each section. Each of these checks asks fill-in-the-blank, matching, and non-computational questions designed to help students learn mathematical terminology and to test basic understanding of that section's concepts.

Algebra and Trigonometry: Real Mathematics, Real People

TABLE OF CONTENTS

CHAPTER P PREREQUISITES.
P.1. Real Numbers. P.2. Exponents and Radicals. P.3. Polynomials and Factoring.
P.4. Rational Expressions. P.5. The Cartesian Plane. P.6. Representing Data Graphically. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics.
1. FUNCTIONS AND THEIR GRAPHS.
Introduction to Library of Functions.1.1 Graphs of Equations. 1.2 Lines in the Plane.
1.3 Functions. 1.4 Graphs of Functions.1.5 Shifting, Reflecting, and Stretching Graphs.
1.6 Combinations of Functions. 1.7 Inverse Functions. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics.
2. SOLVING EQUATIONS AND INEQUALITIES.
2.1 Linear Equations and Problem Solving. 2.2 Solving Equations Graphically. 2.3 Complex Numbers. 2.4 Solving Quadratic Equations Algebraically.
2.5 Solving Other Types of Equations Algebraically. 2.6 Solving Inequalities Algebraically and Graphically. 2.7 Linear Models and Scatter Plots. Chapter Summary.
Review Exercises. Chapter Test. Cumulative Test: Chapters P−2. Proofs in Mathematics. Progressive Summary (Ch P−2).
3. POLYNOMIAL AND RATIONAL FUNCTIONS.
3.1 Quadratic Functions. 3.2 Polynomial Functions of Higher Degree. 3.3 Real Zeros of Polynomial Functions. 3.4 The Fundamental Theorem of Algebra. 3.5 Rational Functions and Asymptotes. 3.6 Graphs of Rational Functions. 3.7 Quadratic Models.
Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics.
4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
4.1 Exponential Functions and Their Graphs . 4.2 Logarithmic Functions and Their Graphs. 4.3 Properties of Logarithms. 4.4 Solving Exponential and Logarithmic Equations. 4.5 Exponential and Logarithmic Models. 4.6 Nonlinear Models. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 3−4. Proofs in Mathematics. Progressive Summary (Ch P−4).
5. TRIGONOMETRIC FUNCTIONS.
5.1 Angles and Their Measure. 5.2 Right Triangle Trigonometry. 5.3 Trigonometric Functions of Any Angle. 5.4 Graphs of Sine and Cosine Functions. 5.5 Graphs of Other Trigonometric Functions. 5.6 Inverse Trigonometric Functions. 5.7 Applications and Models. Chapter Summary. Review Exercises. Chapter Test. Library of Parent Functions Review. Proofs in Mathematics.
6. ANALYTIC TRIGONOMETRY.
6.1 Using Fundamental Identities. 6.2 Verifying Trigonometric Identities. 6.3 Solving Trigonometric Equations. 6.4 Sum and Difference Formulas. 6.5 Multiple-Angle and Product-to-Sum Formulas. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics.
7. ADDITIONAL TOPICS IN TRIGONOMETRY.
7.1 Law of Sines. 7.2 Law of Cosines. 7.3 Vectors in the Plane. 7.4 Vectors and Dot Products. 7.5 Trigonometric Form of a Complex Number. Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 5−7. Proofs in Mathematics.
Progressive Summary (Ch P−7).
8. LINEAR SYSTEMS AND MATRICES.
8.1 Solving Systems of Equations. 8.2 Systems of Linear Equations in Two Variables.
8.3 Multivariable Linear Systems. 8.4 Matrices and Systems of Equations. 8.5 Operations with Matrices. 8.6 The Inverse of a Square Matrix. 8.7 The Determinant of a Square Matrix. 8.8 Applications of Matrices and Determinants. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics.
9. SEQUENCES, SERIES, AND PROBABILITY.
9.1 Sequences and Series. 9.2 Arithmetic Sequences and Partial Sums. 9.3 Geometric Sequences and Series. 9.4 The Binomial Theorem. 9.5 Counting Principles. 9.6 Probability. Chapter Summary. Review Exercises. Chapter Test. Proofs in Mathematics.
10. TOPICS IN ANALYTIC GEOMETRY.
10.1 Circles and Parabolas. 10.2 Ellipses. 10.3 Hyperbolas. 10.4 Parametric Equations. 10.5 Polar Coordinates. 10.6 Graphs of Polar Equations. 10.7 Polar Equations of Conics.
Chapter Summary. Review Exercises. Chapter Test. Cumulative Test: Chapters 8−10.
Proofs in Mathematics. Progressive Summary (Ch P−10).
Appendix A: Technology Support Guide.
Appendix B: Concepts in Statistics (WEB only).
B.1 Measures of Central Tendency and Dispersion. B.2 Least Squares Regression.
Appendix C: Variation (WEB only).
Appendix D: Solving Linear Equations and Inequalities (WEB only).
Appendix E: Systems of Inequalities (WEB only).
E.1 Solving Systems of Inequalities. E.2 Linear Programming.
Appendix F Mathematical Induction (WEB only).

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

Complete Solutions Manual on Instructor's Companion Web Site

ISBN: 9781305252530
This manual contains solutions to all exercises from the text, including Chapter Review Exercises, and Chapter Tests. This manual can be found on the Instructors Companion Site.

Cengage Learning Testing, powered by Cognero Instant Access

ISBN: 9781305259010
Cengage Learning Testing Powered by Cognero is a flexible, online system that allows you to author, edit, and manage test bank content, create multiple test versions in an instant, and deliver tests from your LMS, your classroom or wherever you want. This is available online via the Instructor Companion Site at www.cengage.com/login

Student Solutions Manual

ISBN: 9781305252493
Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.

DVD

ISBN: 9781305252516
Keyed to the text by section, these DVDs provide comprehensive coverage of the course—along with additional explanations of concepts, sample problems, and applications—to help students review essential topics.

FOR STUDENTS

Student Solutions Manual

ISBN: 9781305252493
Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving you a way to check your answers and ensure that you took the correct steps to arrive at an answer.

DVD

ISBN: 9781305252516
These DVDs provide comprehensive, section-by-section coverage of the course—along with additional explanations of concepts, sample problems, and applications—to help you review essential topics and prepare for exams.