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Trigonometry
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PrefaceSupplements Guide 1. Trigonometric Functions1.1 Angles1.2 Angle Relationships and Similar Triangles1.3 Trigonometric Functions1.4 Using the Definitions of the Trigonometric Functions 2. Acute Angles and Right Triangles2.1 Trigonometric Functions of Acute Angles2.2 Trigonometric Functions of Non-Acute Angles2.3 Finding Trigonometric Function Values Using a Calculator2.4 Solving Right Triangles2.5 Further Applications of Right Triangles 3. Radian Measure and the Unit Circle3.1 Radian Measure3.2 Applications of Radian Measure3.3 The Unit Circle and Circular Functions3.4 Linear and Angular Speed 4. Graphs of the Circular Functions4.1 Graphs of the Sine and Cosine Functions4.2 Translations of the Graphs of the Sine and Cosine Functions4.3 Graphs of the Tangent and Cotangent Functions4.4 Graphs of the Secant and Cosecant Functions4.5 Harmonic Motion 5. Trigonometric Identities5.1 Fundamental Identities5.2 Verifying Trigonometric Identities5.3 Sum and Difference Identities for Cosine5.4 Sum and Difference Identities for Sine and Tangent5.5 Double-Angle Identities5.6 Half-Angle Identities 6. Inverse Circular Functions and Trigonometric Equations6.1 Inverse Circular Functions6.2 Trigonometric Equations I6.3 Trigonometric Equations II6.4 Equations Involving Inverse Trigonometric Functions 7. Applications of Trigonometry and Vectors7.1 Oblique Triangles and the Law of Sines7.2 The Ambiguous Case of the Law of Sines7.3 The Law of Cosines7.4 Vectors, Operation, and the Dot Product7.5 Applications of Vectors 8. Complex Numbers, Polar Equations, and Parametric Equations8.1 Complex Numbers8.2 Trigonometric (Polar) Form of Complex Numbers8.3 The Product and Quotient Theorems8.4 De Moivre's Theorem; Powers and Roots of Complex Numbers8.5 Polar Equations and Graphs8.6 Parametic Equations, Graphs, and Applications Appendix A. Equations and InequalitiesAppendix B. Graphs of EquationsAppendix C. FunctionsAppendix D. Graphing Techniques GlossarySolutions to Selected ExercisesAnswers to Selected ExercisesIndex of ApplicationsIndex

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#### About the Author

Marge Lial has always been interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, is now affiliated with American River College. Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have produced some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan. When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching and for mathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons. David Schneider has taught mathematics at universities for over 34 years and has authored 36 books. He has an undergraduate degree in mathematics from Oberlin College and a PhD in mathematics from MIT. During most of his professional career, he was on the faculty of the University of Maryland--College Park. His hobbies include travel, dancing, bicycling, and hiking. Callie Daniels has always had a passion for learning mathematics and brings that passion into the classroom with her students. She attended the University of the Ozarks on an athletic scholarship, playing both basketball and tennis. While there, she earned a bachelor's degree in Secondary Mathematics Education as well as the NAIA Academic All-American Award. She has two master's degrees: one in Applied Mathematics and Statistics from the University of Missouri-Rolla, the second in Adult Education from the University of Missouri- St. Louis. Her hobbies include watching her sons play sports, riding horses, fishing, shooting photographs, and playing guitar. Her professional interests include improving success in the community college mathematics sequence, using technology to enhance students' understanding of mathematics, and creating materials that support classroom teaching and student understanding.