A215832 Decimal expansion of the maximum of the function f(x) = log(cos(sin(x)))/log(sin(cos(x))), x in (0,Pi/2).

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

Offset: 0

Author

Roman Witula, Aug 24 2012

Keywords

• nonn
• cons

Comments

The inverse of this maximum is equal to A215833. The argument z in (0,Pi/2) for which f(z) = max{f(x): x in (0,Pi/2)} is given in A168546. We note that f is increasing in the interval (0,z) and decreasing in the interval (z,Pi/2).

Examples

			We have M := max{f(x): x in (0,Pi/2)} = 0.6410192376327.
		

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. A215833, A168546, A215670, A215668, A216891.