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Reply to Mark Dickinson
Python 3.1.2 -- 32 bit gives sin(2^60) = -0.7391806966492228
PariGp 2.3.4 gives sin(2^60) = -0.8306492176372546505752817956
So it seems Intel's x87 FSIN is not being used.
Application? I don't have one, but it is not too hard to imagine that buried deep in a large simulation, sin(x) is presented with a large argument, and whose wrong result is never noticed until ...
I quote from Ng's paper :
http://www.derekroconnor.net/Software/Ng--ArgReduction.pdf
--------------------------
"It is often argued that being concerned about large arguments
is unnecessary, because sophisticated users simply know better 
than to compute with large angles. It is our contention that this position is suboptimal, because:
 1. It places an unnecessary burden on the user.
 2. The consequences of producing incorrect (inaccurate)answers
 may be catastrophic; many people assume that computers can
 do arithmetic very well. While numerical analysts know better,
 not all programmers are numerical analysts, nor should they be.
 3. It is a vendors responsibility to provide answers that
 are as correct as possible."
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Derek O'Connor