On the Definitions of the Trigonometric Functions (Classic Reprint) - Softcover

Alexander Macfarlane

 
9780282992293: On the Definitions of the Trigonometric Functions (Classic Reprint)

Synopsis

This book delves into the fundamental definitions of trigonometric functions, challenging traditional understandings and presenting a unified framework for a more comprehensive analysis. The author explores the historical development of these functions, from their origins in ancient geometry to the more abstract definitions used in modern mathematical treatises. Through a rigorous examination of various definitions—triangular, circular, and hyperbolic—the author proposes a new system that integrates these different perspectives. This system emphasizes the importance of area in defining trigonometric functions and introduces new concepts such as "trigonometric areas" and "complementary functions." The author's approach provides a deeper understanding of the relationships between trigonometric functions and their applications in various branches of mathematics. The book's insights are essential for anyone seeking a thorough understanding of trigonometry and its role in the broader field of mathematical analysis.

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