As a counterpoint, no real computation I've performed on a computer needed to compute the cos of 2^1023 radians. I can't imagine such a scenario either.
You can either implement the functions accurately or inaccurately. Implementing them inaccurately is a slippery slope. Intel botched the hardware implementations in their processors not only for large inputs but also for inputs nearish to multiples of pi:
http://notabs.org/fpuaccuracy/index.htm