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A215670 Decimal expansion of the min value of F(x) := cos(sin(x)) - sin(cos(x)), x in R. 7
1, 0, 7, 1, 2, 6, 9, 4, 4, 8, 7, 2, 9, 5, 2, 9, 9, 6, 1, 1, 2, 0, 2, 9, 4, 8, 1, 3, 4, 7, 4, 1, 9, 1, 7, 4, 8, 4, 3, 3, 2, 1, 3, 9, 8, 2, 6, 3, 3, 6, 6, 1, 2, 8, 9, 0, 4, 4, 7, 3, 5, 5, 8, 4, 2, 6, 4, 7, 9, 8, 6, 2, 7, 2, 1, 1, 3, 1, 1, 6, 9, 6, 6, 8, 5, 8, 5, 1, 8, 7, 7, 9, 6, 2, 3, 5, 4, 7, 3, 7, 5, 9, 2, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
We note that dF(x)/dx = (-1/2)*h(x)*sin(2*x), x in (0,Pi/2), where h(x) is the function discussed in comments to A215668 (see also Witula et al.'s reference for more informations).
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
FORMULA
F(z) = cos(sin(z)) - sin(cos(z)) = (cos(z) - sin(z))*(cos(cos(z)) + sin(sin(z)))*cos(cos(z))/(cos(sin(z)) + sin(cos(z)))*cos(z) = cos(2*z)*cos(cos(z))^2/(cos(sin(z)) + sin(cos(z)))*cos(z)^2 = (1 - tan(z)^2)*cos(cos(z))^2/(cos(sin(z)) + sin(cos(z))), where z := A215668.
EXAMPLE
min{F(x): x in R} = F(z) = 0.1071269448729529961...
CROSSREFS
Sequence in context: A147708 A238273 A155773 * A010144 A195409 A318353
KEYWORD
nonn,cons
AUTHOR
Roman Witula, Aug 20 2012
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)