Trigonometry, 3rd Edition
October 2011, ©2012
The third edition of Cynthia Young's Trigonometry brings together all the elements that have allowed instructors and learners to successfully "bridge the gap" between classroom instruction and independent homework by overcoming common learning barriers and building confidence in students' ability to do mathematics. Written in a clear voice that speaks to students and mirrors how instructors communicate in lecture, Young's hallmark pedagogy enables students to become independent, successful learners. Varied exercise types and modeling projects keep the learning fresh and motivating. Young continues her tradition of fostering a love for succeeding in mathematics by introducing inquiry-based learning projects in this edition, providing learners an opportunity to master the material with more freedom while reinforcing mathematical skills and intuition.
The seamless integration of Cynthia Young's Trigonometry 3rd edition with WileyPLUS, a research-based, online environment for effective teaching and learning, continues Young's vision of building student confidence in mathematics because it takes the guesswork out of studying by providing them with a clear roadmap: what to do, how to do it, and whether they did it right.
WileyPLUS sold separately from text.
1.1 Angles, Degrees, and Triangles 4
1.2 Similar Triangles 17
1.3 Definition 1 of Trigonometric Functions: Right Triangle Ratios 28
1.4 Evaluating Trigonometric Functions: Exactly and with Calculators 38
1.5 Solving Right Triangles 49
Inquiry-Based Learning Project 63 | Modeling Our World 65 |
Review 67 | Review Exercises 70 | Practice Test 73
2 Trigonometric Functions 74
2.1 Angles in the Cartesian Plane 76
2.2 Definition 2 of Trigonometric Functions: The Cartesian Plane 84
2.3 Evaluating Trigonometric Functions for Nonacute Angles 93
2.4 Basic Trigonometric Identities 110
Inquiry-Based Learning Project 120 | Modeling Our World 121 |
Review 122 | Review Exercises 124 | Practice Test 126 |
Cumulative Test 127
3 Radian Measure and the Unit Circle Approach 128
3.1 Radian Measure 130
3.2 Arc Length and Area of a Circular Sector 141
3.3 Linear and Angular Speeds 151
3.4 Definition 3 of Trigonometric Functions: Unit Circle Approach 159
Inquiry-Based Learning Project 170 | Modeling Our World 171 |
Review 172 | Review Exercises 174 | Practice Test 176 |
Cumulative Test 177
4 Graphing Trigonometric Functions 178
4.1 Basic Graphs of Sine and Cosine Functions: Amplitude and Period 180
4.2 Translations of the Sine and Cosine Functions: Addition of Ordinates 204
4.3 Graphs of Tangent, Cotangent, Secant, and Cosecant Functions 226
Inquiry-Based Learning Project 246 | Modeling Our World 247 |
Review 248 | Review Exercises 251 | Practice Test 254 |
Cumulative Test 255
5 Trigonometric Identities 256
5.1 Trigonometric Identities 258
5.2 Sum and Difference Identities 268
5.3 Double-Angle Identities 281
5.4 Half-Angle Identities 290
5.5 Product-to-Sum and Sum-to-Product Identities 300
Inquiry-Based Learning Project 309 | Modeling Our World 310 |
Review 311 | Review Exercises 313 | Practice Test 316 |
Cumulative Test 317
6 Solving Trigonometric Equations 318
6.1 Inverse Trigonometric Functions 320
6.2 Solving Trigonometric Equations That Involve Only One Trigonometric Function 342
6.3 Solving Trigonometric Equations That Involve Multiple Trigonometric Functions 353
Inquiry-Based Learning Project 360 | Modeling Our World 362 |
Review 363 | Review Exercises 366 | Practice Test 368 |
Cumulative Test 369
7 Applications of Trigonometry: Triangles and Vectors 370
7.1 Oblique Triangles and the Law of Sines 372
7.2 The Law of Cosines 387
7.3 The Area of a Triangle 397
7.4 Vectors 405
7.5 The Dot Product 421
Inquiry-Based Learning Project 429 | Modeling Our World 430 |
Review 431 | Review Exercises 433 | Practice Test 436 |
Cumulative Test 437
8 Complex Numbers, Polar Coordinates, and Parametric Equations 438
8.1 Complex Numbers 440
8.2 Polar (Trigonometric) Form of Complex Numbers 447
8.3 Products, Quotients, Powers, and Roots of Complex Numbers: De Moivre’s Theorem 456
8.4 Polar Equations and Graphs 469
8.5 Parametric Equations and Graphs 483
Inquiry-Based Learning Project 494 | Modeling Our World 495 |
Review 497 | Review Exercises 499 | Practice Test 501 |
Cumulative Test 502
Appendix A Algebraic Prerequisites and Review 503
A.1 Factoring Polynomials 504
A.2 Basic Tools: Cartesian Plane, Distance, and Midpoint 515
A.3 Graphing Equations: Point-Plotting, Intercepts, and Symmetry 523
A.4 Functions 535
A.5 Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change 554
A.6 Graphing Techniques: Transformations 574
A.7 Operations on Functions and Composition of Functions 589
A.8 One-to-One Functions and Inverse Functions 599
Review 614 | Review Exercises 617 | Practice Test 621
Appendix B Conic Sections 623
B.1 Conic Basics 624
B.2 The Parabola 627
B.3 The Ellipse 640
B.4 The Hyperbola 652
B.5 Rotation of Axes 664
B.6 Polar Equations of Conics 674
Review 685 | Review Exercises 688 | Practice Test 691
Answers to Odd Numbered Exercises 692
Applications Index 738
Subject Index 740
- New Applications Added: Applications to Economics, Business, Environmental Science, and Health have been added to each chapter to augment existing applications on Finance, Biology, and Chemistry.
- Inquiry-Based Learning Projects added to every chapter! These projects actively involve students in the learning process, aiding in understanding and mastery of the material.
- Revised and Enriched Exercise Sets Throughout
- Updated “Technology Tips”: Optional technology tips in the margin demonstrate how students can use technology to confirm analytic solutions.
- Clear, Concise and Inviting Writing. The author's engaging and clear presentation is presented in a layout that is designed to reduce math anxiety in students.
- Author Lecture Videos. For review at home or for a class missed, Cynthia Young has recorded over 300 instructional videos including worked examples and "Your Turn" problems from the text. These videos can be found in WileyPLUS and are denoted in the text with an icon.
- WileyPLUS, accompanied with Young, Trigonometry3rd edition, provides a research based, online environment for effective teaching and learning. WileyPLUS builds students’ confidence because it takes the guesswork out of studying by providing students with a clear roadmap: what to do, how to do it, if they did it right.
- Six Different Types of Exercises. Every chapter has skill, application, catch the mistake, challenge, conceptual, and technology exercises. The exercises gradually increase in difficulty and vary skill and conceptual emphasis.
- Correct vs. Incorrect. In addition to standard examples, some problems are worked both correctly and incorrectly to highlight common errors students make. Counter examples, like these, are often an effective learning approach for many students.
- Catch the Mistake. In every section, ‘Catch the Mistake’ exercises put the students in the role of the instructor grading homework which increases the depth of understanding and reinforces what they have learned.
- Your Turn. Students are often asked to work a problem immediately following an example to reinforce and check their understanding. This helps them build confidence as they progress in the chapter. These are ideal for in-class activity and preparing the student to work homework later.
- Parallel Words and Math. This text reverses the common presentation of examples by placing the explanation in words on the left and the mathematics in parallel on the right. This makes it easier for students to read through examples as the material flows more naturally and as commonly presented in lecture.
- Modeling Our World. Found in every chapter, these projects engage students by using real world data to model mathematical applications found in everyday life.
- Chapter Cumulative Test. Included at the end of each chapter to assess and improve students' retention of material.
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