Approximating sinh through taylor's series

  • Thread starter jakey
  • Start date
  • #1
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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!
 

Answers and Replies

  • #2
AlephZero
Science Advisor
Homework Helper
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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???
 

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