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%I #20 Sep 22 2012 10:52:19
%S 6,9,2,7,2,8,5,7,0,1,8,6,8,3,3,8,8,8,3,4,7,3,6,5,2,2,0,5,8,0,2,9,4,0,
%T 3,0,2,3,6,7,7,4,5,4,4,8,3,7,8,5,5,4,6,6,2,5,0,4,6,4,2,6,7,6,4,5,3,9,
%U 7,4,2,4,9,5,6,6,1,6,4,1,6,7,4,4,3,9,5,2,8,3,9,5,2,2,1,4,7,2,8,7,7,8,5,9,8,6,5,5,8
%N Decimal expansion of the zero z in (0,Pi/2) of the function sin(sin(x))/x - cos(cos(x))/x.
%C It is proved (see Witula et al.'s reference) that the function h(x) := sin(sin(x))/x - cos(cos(x))/x is decreasing in the interval (0,Pi/2) and has zero z in (0,Pi/4). We have sin(sin(z))/z = cos(cos(z))/z = 0.933396189408898411846964. Moreover the following relation hold: F(z) = min{F(x): x \in R} = 0.10712694487, where F(x) := cos(sin(x)) - sin(cos(x)) - see also A215670 and the Witula et al.'s reference for more information.
%D R. Witula, D. Jama, E. Hetmaniok, D. Slota, On some inequality of the trigonometric type, Zeszyty Naukowe Politechniki Slaskiej - Matematyka-Fizyka (Science Fascicle of Silesian Technical University - Math.-Phys.), 92 (2010), 83-92.
%e z = 0.692728570186833888... rad (= 39.6904234198376057055880... deg).
%Y Cf. A215670, A215832, A215833, A168546, A216891.
%K nonn,cons
%O 0,1
%A _Roman Witula_, Aug 20 2012