TITLE: how can we convert sin function into continued fraction?
QUESTION [9 upvotes]: how can we convert sin function into continued fraction ?
for example 
http://mathworld.wolfram.com/EulersContinuedFraction.html
how can we convert sin to simmilar continued fraction ?? 
and what about sinh and cosh ? arcsin ? arctan ? cos ? arccos ?? 
in general , how can convert any function to continued fraction ??? 
my friend asked me this question , so i hope that you help me to be enabled to help him
thanx for all of you

REPLY [3 votes]: I learned how to do this from this document (look for Theorem I)
https://people.math.osu.edu/sinnott.1/ReadingClassics/continuedfractions.pdf
Interestingly, this looks to be a translation of Euler's original work. I find him easy to understand, he avoids confusing his message in clumsy notation.