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).

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

Offset: 0

Author

Roman Witula, Aug 24 2012

Keywords

• nonn
• cons

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.

Examples

			= 0.8470252640812533228197751102168942432471525...
		

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.

Crossrefs

Cf. A215832, A215833, A215670, A215668, A216891.

Programs

Mathematica

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

Extensions

Terms corrected by Jean-François Alcover, Feb 11 2013