What exactly is it you think it can't do? It can explain and apply a number of methods for calculating sin. For sin it knows the symmetry and periodicity, and so will treat requests for sin of larger values accordingly. To convince it to continue to write out the numbers for an arbitrary large number of values without emitting "... continue like this" or similar shortcut a human told to do annoyingly pointless repetitive work would also be prone to prefer is indeed tricky, but there's nothing to suggest it can't do it.
