College Trigonometry

by Aufmann, Richard N.; Barker, Vernon C.; Nation, Richard D.

• ISBN13: 9780618388042
• ISBN10: 0618388044
• Edition: 5th
• Format: Hardcover
• Copyright: 2004-04-02
• Publisher: Brooks Cole

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.

Table of Contents

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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