Summary

This text provides a supportive environment to help students successfully learn the content of a standard trigonometry course. By incorporating interactive learning techniques, the Aufmann team helps students to better understand concepts, focus their studying habits, and obtain greater mathematical success. Prerequisite review is include in the textbook (and supporting materials) so that instructors can spend less time covering review material and students can still fill in the gaps in their mathematical knowledge. Integrated Review Notes provided next to examples throughout the text help students see the key prerequisite skills used within the example. For added convenience, these example-specific notes direct students to the page(s) where they can practice and review the skills needed to understand the new concept, thus decreasing students' frustration and increasing their success. Prepare for the Next Section Exercises, found at the end of the exercise sets, have been carefully selected to review the prerequisite skills students will need in the next section. Next to each exercise is a reference to a section of the text where students can go to review topics they don't understand. Answers to all of these exercises are provided in the Answer Appendix to help students better understand what they need to do to prepare for the next section. To create a link between the algebraic and visual representations of a solution, increase students' understanding of the concept presented, and accommodate different learning styles, the authors have provided both an algebraic solution and a graphical solution (represented by either a coordinate grid graph or a graphing calculator screen) for appropriate examples. Focus on Problem Solving at the beginning of every chapter reviews and demonstrates various strategies used by successful problem-solvers. Students become more comfortable with problem-solving and have a collection of tips and strategies to refer to for added support. Special modeling sections throughout the text, which rely heavily on the graphing calculator, provide an opportunity to motivate students with relevant, modern applications. These special sections introduce the idea of mathematical modeling of data through linear, quadratic, exponential, logarithmic, and logistic regression. Students are often required to work with tables, graphs, and charts using data drawn from a variety of disciplines. Rich exercise sets and applications offer instructors a wide range of options when assigning homework, including many that involve real data. When appropriate, the end of a section presents applications that require students to use problem-solving strategies along with the skills covered in that section to solve practical problems. Exercises encourage problem solving, skill building, group work, writing, and appropriate use of graphing calculators. Connecting Concepts exercises found in every exercise set extend some of the concepts discussed in the section and require students to connect ideas studied earlier with new concepts. These more involved, multi-step exercises help students practice problems involving multiple concepts, similar to those found on many exams. Cumulative Review Exercises added to every chapter allow students to review material from previous chapters to better prepare for tests and material to come. The answers for all of these exercises, along with cross-references to the relevant text section, are included in the student answer section of the textbook to enable students' to check their work.

Note: Each chapter concludes with a Summary, True/False Exercises, Review Exercises, and a Test. Chapters 2–7 include Cumulative Review Exercises
Functions and Graphs
Equations and Inequalities
A Two-Dimensional Coordinate System and Graphs
Introduction to Functions
Properties of Graphs
The Algebra of Functions
Inverse Functions
Modeling Data Using Regression
Exploring Concepts with Technology: Graphing Piecewise Functions with a Graphing Calculator
Trigonometric Functions
Angles and Arcs
Trigonometric Functions of Acute Angles
Trigonometric Functions of Any Angle
Trigonometric Functions of Real Numbers
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: Sinusoidal Families
Trigonometric Identities and Equations
Verification of Trigonometric Identities
Sum, Difference, and Cofunction Identities
Double- and Half-Angle Identities
Identities Involving the Sum of Trigonometric Functions
Inverse Trigonometric Functions
Trigonometric Equations
Exploring Concepts with Technology: Approximate an Inverse Trigonometric Function with Polynomials
Applications of Trigonometry
The Law of Sines
The Law of Cosines and Area
Vectors
Exploring Concepts with Technology: Optimal Branching of Arteries
Complex Numbers
Complex Numbers
Trigonometric Form of Complex Numbers
De Moivre's Theorem
Exploring Concepts with Technology: The Mandelbrot Replacement Procedure
Topics in Analytic Geometry
Parabolas
Ellipses
Hyperbolas
Rotation of Axes
Introduction to Polar Coordinates
Polar Equations of the Conics
Parametric Equations
Exploring Concepts with Technology: Using a Graphing Calculator to Find the nth Roots of z
Exponential and Logarithmic Functions
Exponential Functions and Their Applications
Logarithmic Functions and Their Applications
Logarithms and Logarithmic Scales
Exponential and Logarithmic Equations
Exponential Growth and Decay
Modeling Data with Exponential and Logarithmic Functions
Exploring Concepts with Technology: Using a Semilog Graph to Model Exponential Decay
Solutions to the Try Exercises
Answers to Selected Exercises
Index
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