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

Preface
To the Student
Just-In-Time Review



Graphs, Functions, and Models

1.1 Introduction to Graphing

Visualizing the Graph


1.2 Functions and Graphs
1.3 Linear Functions, Slope, and Applications

Visualizing the Graph
Mid-Chapter Mixed Review


1.4 Equations of Lines and Modeling
1.5 Linear Equations, Functions, Zeros, and Applications
1.6 Solving Linear Inequalities



Study Guide
Review Exercises
Test


More on Functions

2.1 Increasing, Decreasing, and Piecewise Functions; Applications
2.2 The Algebra of Functions
2.3 The Composition of Functions

Mid-Chapter Mixed Review


2.4 Symmetry
2.5 Transformations

Visualizing the Graph


2.6 Variation and Application



Study Guide
Review Exercises
Test


Quadratic Functions and Equations; Inequalities

3.1 The Complex Numbers
3.2 Quadratic Equations, Functions, Zeros, and Models
3.3 Analyzing Graphs of Quadratic Functions

Visualizing the Graph
Mid-Chapter Review


3.4 Solving Rational Equations and Radical Equations
3.5 Solving Equations and Inequalities with Absolute Value



Study Guide
Review Exercises
Test


Polynomial Functions and Rational Functions

4.1 Polynomial Functions and Modeling
4.2 Graphing Polynomial Functions

Visualizing the Graph


4.3 Polynomial Division; The Remainder Theorem and the Factor Theorem

Mid-Chapter Mixed Review


4.4 Theorems about Zeros of Polynomial Functions
4.5 Rational Functions

Visualizing the Graph


4.6 Polynomial Inequalities and Rational Inequalities



Study Guide
Review Exercises
Test


Exponential Functions and Logarithmic Functions

5.1 Inverse Functions
5.2 Exponential Functions and Graphs
5.3 Logarithmic Functions and Graphs

Visualizing the Graph
Mid-Chapter Mixed Review


5.4 Properties of Logarithmic Functions
5.5 Solving Exponential Equations and Logarithmic Equations
5.6 Applications and Models: Growth and Decay; Compound Interest



Study Guide
Review Exercises
Test


The Trigonometric Functions

6.1 Trigonometric Functions of Acute Angles
6.2 Applications of Right Triangles
6.3 Trigonometric Functions of Any Angle

Mid-Chapter Mixed Review


6.4 Radians, Arc Length, and Angular Speed
6.5 Circular Functions: Graphs and Properties
6.6 Graphs of Transformed Sine Functions and Cosine Functions



Visualizing the Graph
Study Guide
Review Exercises
Test


Trigonometric Identities, Inverse Functions, and Equations

7.1 Identities: Pythagorean and Sum and Difference
7.2 Identities: Cofunction, Double-Angle, and Half-Angle
7.3 Proving Trigonometric Identities

Mid-Chapter Mixed Review


7.4 Inverses of the Trigonometric Functions
7.5 Solving Trigonometric Equations



Visualizing the Graph
Study Guide
Review Exercises
Test


Applications of Trigonometry

8.1 The Law of Sines
8.2 The Law of Cosines
8.3 Complex Numbers: Trigonometric Notation

Mid-Chapter Mixed Review


8.4 Polar Coordinates and Graphs

Visualizing the Graph


8.5 Vectors and Applications
8.6 Vector Operations



Study Guide
Review Exercises
Test


Systems of Equations and Matrices

9.1 Systems of Equations in Two Variables

Visualizing the Graph


9.2 Systems of Equations in Three Variables
9.3 Matrices and Systems of Equations
9.4 Matrix Operations

Mid-Chapter Mixed Review


9.5 Inverses of Matrices
9.6 Determinants and Cramer’s Rule
9.7 Systems of Inequalities and Linear Programming
9.8 Partial Fractions



Study Guide
Review Exercises
Test


Analytic Geometry Topics

10.1 The Parabola
10.2 The Circle and the Ellipse
10.3 The Hyperbola
10.4 Nonlinear Systems of Equations and Inequalities

Visualizing the Graph
Mid-Chapter Mixed Review


10.5 Rotation of Axes
10.6 Polar Equations of Conics
10.7 Parametric Equations



Study Guide
Review Exercises
Test


Sequences, Series, and Combinatorics

11.1 Sequences and Series
11.2 Arithmetic Sequences and Series
11.3 Geometric Sequences and Series

Visualizing the Graph


11.4 Mathematical Induction

Mid-Chapter Mixed Review


11.5 Combinatorics: Permutations
11.6 Combinatorics: Combinations
11.7 The Binomial Theorem
11.8 Probability



Study Guide
Review Exercises
Test



Photo Credits Answers // Additional Instructor’s Answers Index Index of Applications