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A199952
Decimal expansion of greatest x satisfying x^2 + cos(x) = 3*sin(x).
3
1, 7, 7, 1, 7, 9, 2, 9, 5, 2, 9, 8, 2, 0, 2, 6, 3, 3, 7, 2, 6, 5, 9, 2, 3, 5, 8, 6, 4, 4, 9, 0, 9, 4, 2, 1, 6, 2, 2, 0, 1, 5, 8, 2, 4, 5, 5, 1, 8, 6, 3, 0, 8, 9, 1, 8, 9, 2, 1, 1, 4, 7, 0, 0, 9, 3, 4, 5, 2, 5, 6, 5, 1, 6, 7, 0, 3, 5, 0, 8, 1, 3, 9, 7, 8, 1, 6, 1, 4, 4, 3, 8, 7, 0, 4, 5, 5, 8, 7
OFFSET
1,2
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: 0.36356053985895926625732148372284398566895...
greatest x: 1.771792952982026337265923586449094216220...
MATHEMATICA
a = 1; b = 1; c = 3;
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, .36, .37}, WorkingPrecision -> 110]
RealDigits[r] (* A199951 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.77, 1.78}, WorkingPrecision -> 110]
RealDigits[r] (* A199952 *)
PROG
(PARI) a=1; b=1; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018
CROSSREFS
Cf. A199949.
Sequence in context: A146322 A011376 A011452 * A093781 A232649 A232650
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 12 2011
STATUS
approved