Recurrent proofs of the irrationality of certain trigonometric values
classification
🧮 math.NT
math.HO
keywords
elementaryirrationalitynonzeroproofsrationalvaluescertainconsequences
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We use recurrences of integrals to give new and elementary proofs of the irrationality of pi, tan(r) for all nonzero rational r, and cos(r) for all nonzero rational r^2. Immediate consequences to other values of the elementary transcendental functions are also discussed.
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