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A200013
Decimal expansion of greatest x satisfying x^2 - cos(x) = 2*sin(x).
3
1, 4, 5, 0, 9, 3, 8, 4, 4, 9, 6, 3, 4, 9, 7, 4, 4, 3, 1, 1, 2, 8, 2, 8, 5, 5, 7, 6, 6, 9, 0, 3, 5, 7, 7, 3, 8, 9, 4, 4, 7, 4, 8, 7, 0, 1, 1, 5, 3, 4, 6, 3, 9, 8, 7, 6, 5, 4, 2, 3, 5, 8, 6, 2, 6, 2, 9, 6, 1, 9, 2, 8, 4, 3, 0, 8, 1, 3, 5, 0, 5, 9, 1, 7, 2, 0, 8, 4, 3, 0, 4, 9, 7, 0, 9, 4, 6, 6, 0
OFFSET
1,2
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: -0.3941241928589759600997053993545900...
greatest x: 1.450938449634974431128285576690357...
MATHEMATICA
a = 1; b = -1; c = 2;
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, -.4, -.3}, WorkingPrecision -> 110]
RealDigits[r] (* A200012 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
RealDigits[r] (* A200013 *)
PROG
(PARI) a=1; b=-1; c=2; 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: A360962 A320162 A354068 * A178219 A322232 A232397
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 12 2011
STATUS
approved