prove that sin(1) (one radian) is irrational.

Hint start with taylor series expansion

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- Nov 18th 2009, 10:22 AMscubasteve123prove irrational
prove that sin(1) (one radian) is irrational.

Hint start with taylor series expansion - Nov 18th 2009, 11:37 AMjames_bond
Without Taylor-series see this on the 3rd page (7***).

- Nov 19th 2009, 07:31 PMNonCommAlg
you first need this basic and simple fact about alternating series that if then

now suppose for some let

thus is an integer. i'll show that this is false, i.e. cannot be an integer: using the MacLaurine expansion of we have:

it's clear by that we also have:

therefore and so is not an integer. Q.E.D.