What is #cos 2^@# ?
1 Answer
Explanation:
Note that the trigonometric functions of any integer multiple of
We can effectively calculate approximations for the
So:
#sin x = x/(1!)-x^3/(3!)+x^5/(5!)-x^7/(7!)+...#
#cos x = 1/(0!)-x^2/(2!)+x^4/(4!)-x^6/(6!)+...#
We can also use the accurate approximation:
#pi ~~ 355/113#
So:
#2^@ = 2/180*pi ~~ 355/(90*113) = 71/2034# radians
Then:
#cos 2^@ ~~ cos (71/2034)#
#color(white)(cos 2^@) ~~ 1-71^2/(2*2034^2)+71^4/(24*2034^4)#
#color(white)(cos 2^@) ~~ 0.99939083#