E561 -- Variae observationes circa angulos in progressione geometrica progredientes

(Various observations about angles proceeding in geometric progression)

Summary:

From sin(2f) = 2sin f cos f, he gets the infinite product sin f = f cos(f/2) cos(f/4) cos(f/8) cos(f/16).... He reciprocates, and by logarithmic differentiation, gets an infinite sum for 1/f involving cotangents and tangents.

According to the records, it was presented to the St. Petersburg Academy on November 15, 1773.

Publication:

Originally published in Opuscula Analytica 1, 1783, pp. 345-352
Opera Omnia: Series 1, Volume 15, pp. 498 - 508

Documents Available:

Original Publication: E561
An English translation of this article has been done by Jordan Bell: E561.

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