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Learning Trigonometry By Problem Solving [Pehme köide]

(-), (City Univ Of New York, Usa)
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In this book, trigonometry is presented mainly through the solution of specific problems. The problems are meant to help the reader consolidate their knowledge of the subject. In addition, they serve to motivate and provide context for the concepts, definitions, and results as they are presented. In this way, it enables a more active mastery of the subject, directly linking the results of the theory with their applications. Some historical notes are also embedded in selected chapters. The problems in the book are selected from a variety of disciplines, such as physics, medicine, architecture, and so on. They include solving triangles, trigonometric equations, and their applications. Taken together, the problems cover the entirety of material contained in a standard trigonometry course which is studied in high school and college. We have also added some interesting, in our opinion, entertainment problems. To solve them, no special knowledge is required. While they are not directly related to the subject of the book, they reflect its spirit and contribute to a more lighthearted reading of the material.



"In this book, trigonometry is presented mainly through the solution of specific problems. The problems are meant to help the reader consolidate their knowledge of the subject. In addition, they serve to motivate and provide context for the concepts, definitions, and results as they are presented. In this way, it enables a more active mastery of the subject, directly linking the results of the theory with their applications. Some historical notes are also embedded in selected chapters. The problems in the book are selected from a variety of disciplines, such as physics, medicine, architecture, and so on. They include solving triangles, trigonometric equations, and their applications. Taken together, the problems cover the entirety of material contained in a standard trigonometry course which is studied in high school and college. We have also added some interesting, in our opinion, entertainment problems. To solve them, no special knowledge is required. While they are not directly related to the subject of the book, they reflect its spirit and contribute to a more lighthearted reading of the material"--
Preface v
About the Authors ix
Chapter 1 Introduction to Trigonometric Functions
1(16)
Chapter 2 Solving Right Triangles
17(16)
Chapter 3 Trigonometric Properties in Right Triangles
33(14)
Chapter 4 General Definitions of Trigonometric Functions
47(16)
Chapter 5 Basic Properties of General Trigonometric Functions. Methods for Reducing to Acute Angles
63(14)
Chapter 6 Solving Oblique Triangles: Law of Sines
77(16)
Chapter 7 Solving Oblique Triangles: Law of Cosines
93(12)
Chapter 8 Addition and Double Angle Formulas
105(16)
Chapter 9 Product, Sum, and Difference of Trigonometric Functions
121(12)
Chapter 10 Radian Measure
133(16)
Chapter 11 Graphs of Sine and Cosine
149(18)
Chapter 12 Sinusoidal Functions
167(14)
Chapter 13 Applications of Sinusoids
181(10)
Chapter 14 Graphs of Tangent and Cotangent
191(14)
Chapter 15 Basic Sine Equation and Inverse Sine Function
205(16)
Chapter 16 Inverse Cosine and Tangent. Basic Trigonometric Equations for Cosine and Tangent
221(14)
Chapter 17 Trigonometric Identities, Inequalities, and Equations
235(12)
Chapter 18 Applications to Geometry
247(18)
Chapter 19 Historical Background of Complex Numbers. Cardano's Formula
265(14)
Chapter 20 Definition and Properties of Complex Numbers
279(18)
Appendix: Two Remarkable Triangles 297(6)
Summary of Results 303(10)
Answers and Solutions to Problems and Exercises 313(52)
Index 365