A215668 Decimal expansion of the zero z in (0,Pi/2) of the function sin(sin(x))/x - cos(cos(x))/x.

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

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

Table of n, a(n) for n=0..108.

Example

z = 0.692728570186833888... rad  (= 39.6904234198376057055880... deg).

Crossrefs

Cf. A215670, A215832, A215833, A168546, A216891.

Sequence in context: A254135 A198676 A198616 * A344230 A010502 A254292

Adjacent sequences: A215665 A215666 A215667 * A215669 A215670 A215671

Keyword

nonn,cons

Author

Roman Witula, Aug 20 2012

Status

approved