Algebra and Trigonometry

Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University—Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana, with his wife, Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.  Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University—Purdue University Indianapolis. In addition to her career in textbook publishing, she spends time traveling, enjoying her grandchildren, and promoting charity projects for a children's camp.  David Ellenbogen has taught math at the college level for twenty-two years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has also taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges since 1985, having served on its Developmental Mathematics Committee and as a delegate, and has been a member of the Mathematical Association of America since 1979. He has authored dozens of publications on topics ranging from prealgebra to calculus and has delivered lectures at numerous conferences on the use of language in mathematics. Professor Ellenbogen received his BA in mathematics from Bates College and his MA in community college mathematics education from The University of Massachusetts at Amherst. A co-founder of the Colchester Vermont Recycling Program, Professor Ellenbogen has a deep love for the environment and the outdoors, especially in his home state of Vermont. In his spare time, he enjoys playing keyboard in the band Soularium, volunteering as a community mentor, hiking, biking, and skiing. He has two sons, Monroe and Zack.  Judy Penna received her undergraduate degree in mathematics from Kansas State University and her graduate degree in mathematics from the University of Illinois. Since then, she has taught at Indiana University—Purdue University Indianapolis and at Butler University, and continues to focus on writing quality textbooks for undergraduate mathematics students. In her free time she likes to travel, read, knit, and spend time with her children.

• Table of Contents PrefaceTo the StudentJust-In-Time Review Graphs, Functions, and Models 1.1 Introduction to Graphing Visualizing the Graph1.2 Functions and Graphs1.3 Linear Functions, Slope, and Applications Visualizing the GraphMid-Chapter Mixed Review1.4 Equations of Lines and Modeling1.5 Linear Equations, Functions, Zeros, and Applications1.6 Solving Linear Inequalities Study GuideReview ExercisesTestMore on Functions 2.1 Increasing, Decreasing, and Piecewise Functions; Applications2.2 The Algebra of Functions2.3 The Composition of Functions Mid-Chapter Mixed Review2.4 Symmetry2.5 Transformations Visualizing the Graph2.6 Variation and Application Study GuideReview ExercisesTestQuadratic Functions and Equations; Inequalities 3.1 The Complex Numbers3.2 Quadratic Equations, Functions, Zeros, and Models3.3 Analyzing Graphs of Quadratic Functions Visualizing the GraphMid-Chapter Review3.4 Solving Rational Equations and Radical Equations3.5 Solving Equations and Inequalities with Absolute Value Study GuideReview ExercisesTestPolynomial Functions and Rational Functions 4.1 Polynomial Functions and Modeling4.2 Graphing Polynomial Functions Visualizing the Graph4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem Mid-Chapter Mixed Review4.4 Theorems about Zeros of Polynomial Functions4.5 Rational Functions Visualizing the Graph4.6 Polynomial Inequalities and Rational Inequalities Study GuideReview ExercisesTestExponential Functions and Logarithmic Functions 5.1 Inverse Functions5.2 Exponential Functions and Graphs5.3 Logarithmic Functions and Graphs Visualizing the GraphMid-Chapter Mixed Review5.4 Properties of Logarithmic Functions5.5 Solving Exponential Equations and Logarithmic Equations5.6 Applications and Models: Growth and Decay; Compound Interest Study GuideReview ExercisesTestThe Trigonometric Functions 6.1 Trigonometric Functions of Acute Angles6.2 Applications of Right Triangles6.3 Trigonometric Functions of Any Angle Mid-Chapter Mixed Review6.4 Radians, Arc Length, and Angular Speed6.5 Circular Functions: Graphs and Properties6.6 Graphs of Transformed Sine Functions and Cosine Functions Visualizing the GraphStudy GuideReview ExercisesTestTrigonometric Identities, Inverse Functions, and Equations 7.1 Identities: Pythagorean and Sum and Difference7.2 Identities: Cofunction, Double-Angle, and Half-Angle7.3 Proving Trigonometric Identities Mid-Chapter Mixed Review7.4 Inverses of the Trigonometric Functions7.5 Solving Trigonometric Equations Visualizing the GraphStudy GuideReview ExercisesTestApplications of Trigonometry 8.1 The Law of Sines8.2 The Law of Cosines8.3 Complex Numbers: Trigonometric Notation Mid-Chapter Mixed Review8.4 Polar Coordinates and Graphs Visualizing the Graph8.5 Vectors and Applications8.6 Vector Operations Study GuideReview ExercisesTestSystems of Equations and Matrices 9.1 Systems of Equations in Two Variables Visualizing the Graph9.2 Systems of Equations in Three Variables9.3 Matrices and Systems of Equations9.4 Matrix Operations Mid-Chapter Mixed Review9.5 Inverses of Matrices9.6 Determinants and Cramer’s Rule9.7 Systems of Inequalities and Linear Programming9.8 Partial Fractions Study GuideReview ExercisesTestAnalytic Geometry Topics 10.1 The Parabola10.2 The Circle and the Ellipse10.3 The Hyperbola10.4 Nonlinear Systems of Equations and Inequalities Visualizing the GraphMid-Chapter Mixed Review10.5 Rotation of Axes10.6 Polar Equations of Conics10.7 Parametric Equations Study GuideReview ExercisesTestSequences, Series, and Combinatorics 11.1 Sequences and Series11.2 Arithmetic Sequences and Series11.3 Geometric Sequences and Series Visualizing the Graph11.4 Mathematical Induction Mid-Chapter Mixed Review11.5 Combinatorics: Permutations11.6 Combinatorics: Combinations11.7 The Binomial Theorem11.8 Probability Study GuideReview ExercisesTestPhoto Credits Answers // Additional Instructor’s Answers Index Index of Applications