

A168546


Decimal expansion of the argument z in (0,Pi/2) for which the function log(cos(sin(x)))/log(sin(cos(x))) possesses the maximum in (0,Pi/2).


7



8, 4, 7, 0, 2, 5, 2, 6, 4, 0, 8, 1, 2, 5, 3, 3, 2, 2, 8, 1, 9, 7, 7, 5, 1, 1, 0, 2, 1, 6, 8, 9, 4, 2, 4, 3, 2, 4, 7, 1, 5, 2, 5, 0, 7, 4, 2, 9, 1, 8, 6, 5, 4, 2, 3, 7, 9, 6, 2, 1, 7, 1, 6, 8, 1, 7, 8, 1, 8, 9, 1, 2, 7, 3, 5, 9, 9, 4, 0, 4, 4, 3, 0, 7, 3, 4, 4, 9, 9, 3, 7, 6, 4, 0, 5, 8, 5, 2, 0, 3, 5, 4, 1, 5, 8, 4
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OFFSET

0,1


COMMENTS

We have max{f(x): x in (0,Pi/2)} = f(z) = A215832 = 0.641019237..., where f(x) = log(cos(sin(x)))/log(sin(cos(x))). See also A215833.


REFERENCES

R. Witula, D. Jama, E. Hetmaniok, D. Slota, On some inequality of the trigonometric type, Zeszyty Naukowe Politechniki Slaskiej  MatematykaFizyka (Science Fascicle of Silesian Technical University  Math.Phys.), 92 (2010), 8392.


LINKS

Table of n, a(n) for n=0..105.


EXAMPLE

= 0.8470252640812533228197751102168942432471525...


MATHEMATICA

f[x_] := Log[Cos[Sin[x]]] / Log[Sin[Cos[x]]]; x /. FindRoot[f'[x] == 0, {x, 1}, WorkingPrecision > 130] // RealDigits[#, 10, 126]& // First (* JeanFrançois Alcover, Feb 11 2013 *)


CROSSREFS

Cf. A215832, A215833, A215670, A215668, A216891.
Sequence in context: A090325 A090469 A322743 * A195346 A096427 A176453
Adjacent sequences: A168543 A168544 A168545 * A168547 A168548 A168549


KEYWORD

nonn,cons


AUTHOR

Roman Witula, Aug 24 2012


EXTENSIONS

Terms corrected by JeanFrançois Alcover, Feb 11 2013


STATUS

approved



