Abstract

For most of our students, trigonometric identities appear as if by magic. A recent class activity gave me the rare opportunity to lead my students to discover what appears to be a new trigonometric identity by using a combination of graphical, numerical, and algebraic tools. In this article, I demonstrate this result and then show how it can be extended to a wider class of apparently new identities that are all extensions of the Pythagorean identity.

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