A200108 Decimal expansion of greatest x satisfying 2*x^2 - cos(x) = sin(x).

8, 4, 0, 2, 6, 3, 5, 1, 7, 7, 1, 5, 7, 6, 7, 8, 9, 9, 3, 4, 7, 9, 7, 3, 4, 9, 9, 6, 4, 8, 3, 5, 5, 7, 9, 7, 3, 6, 5, 0, 2, 5, 3, 9, 0, 5, 3, 5, 1, 5, 2, 6, 6, 1, 1, 7, 3, 5, 4, 3, 6, 3, 9, 2, 5, 1, 7, 4, 5, 5, 5, 6, 5, 3, 6, 2, 5, 0, 2, 1, 5, 6, 7, 8, 0, 3, 5, 1, 8, 3, 7, 2, 4, 6, 3, 0, 2, 7, 7

Offset

0,1

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Example

least x: -0.4690323711198093057335493058025105005500...
greatest x: 0.840263517715767899347973499648355797365...

Mathematica

a = 2; b = -1; c = 1;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /.
  FindRoot[f[x] == g[x], {x, -.47, -.46}, WorkingPrecision -> 110]
RealDigits[r]  (* A200107 *)
r = x /. FindRoot[f[x] == g[x], {x, .84, .85}, WorkingPrecision -> 110]
RealDigits[r]  (* A200108 *)

Prog

(PARI) a=2; b=-1; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 25 2018

Crossrefs

Cf. A199949.

Sequence in context: A175040 A238292 A350219 * A088397 A021123 A364945

Adjacent sequences: A200105 A200106 A200107 * A200109 A200110 A200111

Keyword

nonn,cons

Author

Clark Kimberling, Nov 13 2011

Status

approved