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 A215668 Decimal expansion of the zero z in (0,Pi/2) of the function sin(sin(x))/x - cos(cos(x))/x. 7
 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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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. REFERENCES 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. LINKS EXAMPLE z = 0.692728570186833888... rad  (= 39.6904234198376057055880... deg). CROSSREFS Cf. A215670, A215832, A215833, A168546, A216891. Sequence in context: A254135 A198676 A198616 * A010502 A254292 A188618 Adjacent sequences:  A215665 A215666 A215667 * A215669 A215670 A215671 KEYWORD nonn,cons AUTHOR Roman Witula, Aug 20 2012 STATUS approved

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Last modified September 19 18:59 EDT 2020. Contains 337182 sequences. (Running on oeis4.)