Are there any proofs for the (ir)rationality of the numbers $\sin(e)$, $\cos(e)$, $\tan(e)$, and $\cot(e)$? Thanking in advance for any references.

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    $\begingroup$ This may be related to the algebraic independence of $\pi$ and $e$. $\endgroup$ – D_S Jul 13 '17 at 10:07
  • $\begingroup$ As a complete outsider to the field, I would guess that the transcendence of special constructs like these is completely unknown. $\endgroup$ – Lubin Apr 3 '18 at 3:11

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