E128 -- Methodus facilis computandi angulorum sinus ac tangentes tam naturales quam artificiales

(An easy method for computing the natural and artificial sines and tangents of angles)


Euler considers a kind of "shifted" sum of reciprocals of squares, 1/(1 ± p) ± 1/(4 ± p) ± 1/(9 ± p) ± 1/(16 ± p) ± .... He uses this to evaluate some sines, cosines log sines, log cosines, tangents and cotangents to 20 decimal places.

According to the records, it was presented to the St. Petersburg Academy on December 15, 1739.

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