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A200280
Decimal expansion of greatest x satisfying 3*x^2 - 4*cos(x) = 2*sin(x).
3
1, 0, 9, 6, 4, 0, 6, 9, 9, 2, 4, 2, 1, 2, 6, 7, 9, 4, 7, 2, 2, 1, 9, 8, 7, 6, 8, 1, 3, 1, 4, 0, 2, 0, 2, 2, 9, 8, 2, 3, 2, 2, 7, 4, 2, 6, 9, 9, 9, 1, 0, 5, 7, 2, 0, 4, 6, 6, 1, 8, 9, 3, 1, 7, 4, 9, 4, 3, 5, 6, 1, 2, 7, 3, 8, 5, 4, 7, 7, 3, 2, 9, 1, 5, 8, 4, 9, 3, 8, 2, 9, 1, 5, 0, 3, 7, 5, 9, 3
OFFSET
1,3
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: -0.73563807644468208614776955612311...
greatest x: 1.096406992421267947221987681314...
MATHEMATICA
a = 3; b = -4; c = 2;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.74, -.73}, WorkingPrecision -> 110]
RealDigits[r] (* A200279 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
RealDigits[r] (* A200280 *)
PROG
(PARI) a=3; b=-4; c=2; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 07 2018
CROSSREFS
Cf. A199949.
Sequence in context: A241993 A099817 A262701 * A198363 A331550 A253267
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 15 2011
STATUS
approved