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.
Contents:
- Preface
- About the Authors
- Introduction to Trigonometric Functions
- Solving Right Triangles
- Trigonometric Properties in Right Triangles
- General Definitions of Trigonometric Functions
- Basic Properties of General Trigonometric Functions. Methods for Reducing to Acute Angles
- Solving Oblique Triangles: Law of Sines
- Solving Oblique Triangles: Law of Cosines
- Addition and Double Angle Formulas
- Product, Sum, and Difference of Trigonometric Functions
- Radian Measure
- Graphs of Sine and Cosine
- Sinusoidal Functions
- Applications of Sinusoids
- Graphs of Tangent and Cotangent
- Basic Sine Equation and Inverse Sine Function
- Inverse Cosine and Tangent. Basic Trigonometric Equations for Cosine and Tangent
- Trigonometric Identities, Inequalities, and Equations
- Applications to Geometry
- Historical Background of Complex Numbers. Cardano's Formula
- Definition and Properties of Complex Numbers
- Appendix: Two Remarkable Triangles
- Summary of Results
- Answers and Solutions to Problems and Exercises
- Index
Readership: Students and Mathematics instructors at high school, undergraduate students.
Key Features:
- The style is informal, non-intimidating, and even entertaining, without sacrificing mathematical rigor
- Full of tips and shortcuts (for example, learn one funny rule, instead of memorizing 16 reduction formulas)
- Wealth of examples with detailed, conceptual explanations to build a strong foundation
