A200110 Decimal expansion of greatest x satisfying 2*x^2 - cos(x) = 2*sin(x).

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

Offset: 1

Author

Clark Kimberling, Nov 13 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least x: -0.35236500577732645310286619535999...
greatest x: 1.0566983769428781221924083031175250...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A199949.

Programs

Mathematica

a = 2; b = -1; c = 2;
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, -.36, -.35}, WorkingPrecision -> 110]
RealDigits[r]  (* A200109 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.05, 1.06}, WorkingPrecision -> 110]
RealDigits[r]  (* A200110 *)

PARI

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