Symbol or number	Approximative value	Realizing simplified expression	Error of expression	Source * *The name below does not indicate necessarily the author of the expression - this is just telling a word of thanks to  those, who helped to extend this collection
	3.141....	355/113	8.5E-8	EVORAN
	1.414....	19601/13860	1.5E-9	EVORAN
	1.732....	18817/10864	1.1E-9	EVORAN
	3.162....	22936/7253	5.7E-9	EVORAN
e	2.718....	28667/10546	5.5E-9	EVORAN
12th	1.059....	26797/25293	1.0E-9	EVORAN

Approximation	Error of expression	Notes	Source see note above
sin(x) = x - (  / 3! ) + ( / 5! ) - (  / 7! ) + (  / 9! )	312.0E-9	note 1	EVORAN
cos(x) = 1 - (  / 2! ) + (  / 4! ) - (  / 6! ) + (  / 8! )	???		EVORAN
tg(x) =
arcsin(x) =
arccos(x) =
arctan(x) = 0.318253x + 0.003314 - 0.130908 + 0.068542 - 0.009159	???	note 2	EVORAN

Note 1: Can be used if x / 4. Error may be reduced to 1.753E-9 by using one more term.
Note 2: If x  1, the following formula should be used: arctan(x) = 0.5 - arctan(1/x)