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A200011
Decimal expansion of greatest x satisfying x^2 - cos(x) = sin(x).
3
1, 1, 4, 9, 5, 5, 4, 6, 2, 7, 2, 7, 7, 4, 7, 3, 1, 8, 9, 0, 6, 9, 5, 2, 2, 4, 9, 4, 7, 4, 4, 4, 0, 9, 0, 2, 0, 1, 1, 3, 9, 6, 8, 1, 7, 7, 9, 1, 3, 9, 2, 4, 4, 8, 1, 3, 1, 9, 2, 5, 2, 4, 8, 6, 3, 4, 8, 5, 5, 1, 5, 3, 5, 9, 0, 5, 7, 3, 7, 8, 3, 9, 3, 2, 6, 2, 5, 3, 2, 9, 9, 1, 6, 6, 5, 1, 2, 9, 2
OFFSET
1,3
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: -0.560987729235911375277437028533668231799...
greatest x: 1.14955462727747318906952249474440902011...
MATHEMATICA
a = 1; b = -1; c = 1;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.6, -.5}, WorkingPrecision -> 110]
RealDigits[r] (* A200010 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
RealDigits[r] (* A200011 *)
PROG
(PARI) a=1; b=-1; c=1; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018
CROSSREFS
Cf. A199949.
Sequence in context: A070434 A011003 A344078 * A200241 A243710 A242610
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 12 2011
STATUS
approved