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Ursinus College

Educational Methods

2017

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A Genetic Context For Understanding The Trigonometric Functions, Danny Otero Mar 2017

A Genetic Context For Understanding The Trigonometric Functions, Danny Otero

Pre-calculus and Trigonometry

In this project, we explore the genesis of the trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant. The goal is to provide the typical student in a pre-calculus course some context for understanding these concepts that is generally missing from standard textbook developments. Trigonometry emerged in the ancient Greek world (and, it is suspected, independently in China and India as well) from the geometrical analyses needed to solve basic astronomical problems regarding the relative positions and motions of celestial objects. While the Greeks (Hipparchus, Ptolemy) recognized the usefulness of tabulating chords of central angles in a circle as aids ...