Approximating sinh through taylor's series

[jakey]

Hi guys,

I want to approximate sinh(3391014490) using taylor's series as i don't know of a way to compute this in c++ (Even NTL can't handle this much).

How could I compute the number of terms I need to sum so that the error is within 10^-10?

Any suggestions? thanks!

 

[AlephZero]

sinh x = (e^x - e^-x)/2

So for x >> 1

sinh x is approximately (e^x)/2

sinh(3391014490) will have about 3391014490 x log_10(e) decimal digits
which is more than 10^9 digits. Are you sure you want to calculate this to 10 decimal places?