Cover image for Trigonometry
Title:
Trigonometry
Author:
Dugopolski, Mark.
Personal Author:
Publication Information:
Boston : Addison-Wesley, [2003]

©2003
Physical Description:
xvi, 368 pages, A-1-A-24 pages, C-1, I-1-I-4 pages : illustrations (some color) ; 26 cm
Language:
English
Subject Term:
ISBN:
9780201703382
Format :
Book

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Library
Call Number
Material Type
Home Location
Status
Central Library QA531 .D764 2003 Adult Non-Fiction Non-Fiction Area
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Summary

Summary

This text is designed for a variety of students with different mathematical needs. For those students who will take additional mathematics, the text will provide the proper foundation of skills, understanding, and insights necessary for success in further courses. For those students who will not pursue further mathematics, the extensive emphasis on applications and modeling will demonstrate the usefulness and applicability of mathematics in the world today. Many of the applied problems in this text are actually real problems that people have had to solve on the job. With an emphasis on problem solving, this text provides students with an excellent opportunity to sharpen their reasoning and thinking skills. With increased critical thinking skills, students will have the confidence they need to tackle whatever future problems they may encounter inside and outside the classroom.

This text is technology optional. With this approach, teachers will be able to offer either a technology-oriented course or a course that does not make use of technology. For departments requiring both options, this text provides the advantage of flexibility.


Author Notes

Mark Dugopolski was born in Menominee, Michigan. After receiving a B.S. from Michigan State University, he taught high school for four years, and then went on to receive an M.S. in mathematics from Northern Illinois University. He also received a Ph.D. in the area of topology from the University of Illinois at Champaign-Urbana, and ever since, Mark has been teaching at Southeastern Louisiana in Hammond, LA. He has been writing textbooks for about fifteen years. He is married and has two daughters, and enjoys playing tennis, jogging, and riding his bicycle in his spare time. Despite the presence of sailboats both on and in his precalculus textbooks, Mark does not sail-- it's his passion for showing students how mathematics is used in the real world that led him to the world of sailing.


Table of Contents

Prefacep. vii
Supplements Listp. xi
Function Galleryp. xv
P Algebraic Prerequisites
P.1 The Cartesian Coordinate Systemp. 2
P.2 Functionsp. 12
P.3 Families of Functions, Transformations, and Symmetryp. 20
P.4 Compositions and Inversesp. 31
Chapter P Highlightsp. 41
Chapter P Review Exercisesp. 42
Chapter P Testp. 44
1 Angles and the Trigonometric Functions
1.1 Angles and Degree Measurep. 46
1.2 Radian Measure, Arc Length, and Areap. 55
1.3 Angular and Linear Velocityp. 66
1.4 The Trigonometric Functionsp. 72
1.5 Right Triangle Trigonometryp. 83
1.6 The Fundamental Identity and Reference Anglesp. 98
Chapter 1 Highlightsp. 106
Chapter 1 Review Exercisesp. 108
Chapter 1 Testp. 110
2 Graphs of the Trigonometric Functions
2.1 The Unit Circle and Graphingp. 112
2.2 The General Sine Wavep. 125
2.3 Graphs of the Secant and Cosecant Functionsp. 137
2.4 Graphs of the Tangent and Contangent Functionsp. 143
2.5 Combining Functionsp. 154
Chapter 2 Highlightsp. 161
Chapter 2 Review Exercisesp. 162
Chapter 2 Testp. 163
Tying it all Togetherp. 164
3 Trigonometric Identities
3.1 Basic Identitiesp. 167
3.2 Verifying Identitiesp. 177
3.3 Sum and Difference Identities for Cosinep. 185
3.4 Sum and Difference Identities for Sine and Tangentp. 192
3.5 Double-Angle and Half-Angle Identitiesp. 198
3.6 Product and Sum Identitiesp. 208
Chapter 3 Highlightsp. 218
Chapter 3 Review Exercisesp. 219
Chapter 3 Testp. 221
Tying it all Togetherp. 222
4 Solving Conditional Trigonometric Equations
4.1 The Inverse Trigonometric Functionsp. 224
4.2 Basic Sine, Cosine, and Tangent Equationsp. 235
4.3 Multiple Angle Equationsp. 249
4.4 Trigonometric Equations of Quadratic Typep. 255
Chapter 4 Highlightsp. 262
Chapter 4 Review Exercisesp. 263
Chapter 4 Testp. 265
Tying it all Togetherp. 266
5 Applications of Trigonometry
5.1 The Law of Sinesp. 268
5.2 The Law of Cosinesp. 280
5.3 Area of a Trianglep. 291
5.4 Vectorsp. 298
5.5 Applications of Vectorsp. 310
Chapter 5 Highlightsp. 320
Chapter 5 Review Exercisesp. 321
Chapter 5 Testp. 323
Tying it all Togetherp. 323
6 Complex Numbers, Polar Coordinates, and Parametric Equations
6.1 Complex Numbersp. 325
6.2 Trigonometric Form of Complex Numbersp. 333
6.3 Powers and Roots of Complex Numbersp. 341
6.4 Polar Equationsp. 347
6.5 Parametric Equationsp. 358
Chapter 6 Highlightsp. 363
Chapter 6 Review Exercisesp. 364
Chapter 6 Testp. 366
Tying it all Togetherp. 366
Appendix A Solutions to Try This Exercisesp. S-1
Appendix B More Thinking Outside the Boxp. S-15
Answers to Selected Exercisesp. A-1
Creditsp. C-1
Index of Applicationsp. I-1
Indexp. I-3

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