Stathis, my recommendation would be to use the double precison sin/cos functions provided along with the Intel compiler. These do a fully accurate argument reduction based on the Payne-Hanek algorithm. The X87 FSIN/FCOS instructions do handle arguments up to 2^63, but use an internal 66 bit value of pi to do the argument reduction. Because only 66 bits of pi are used to perform the reduction, the final computed result may very well be different than if a fully accurate pi is used. This probably explains why you're seeing different results.
I will need to check with John ... not sure that exp (note that itisnt an x87 transcendental operation) was ever formally verified but techniques similar to those described in http://download.intel.com/technology/itj/q41999/pdf/transendental.pdf, and more specifically papers by Peter Tang - nicely described by J. M. Mueller Elementary functions: algorithms and implementation, Birkhaser, 1997 provide an indication of the techniques used to verify accuracy.