A200228 Decimal expansion of greatest x satisfying 3*x^2 - cos(x) = 4*sin(x).

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

Offset: 1

Author

Clark Kimberling, Nov 14 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least x: -0.21220726159791829897823740501037540...
greatest x: 1.164720132600086548144173603917629...
		

Links

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

Crossrefs

Cf. A199949.

Programs

Mathematica

a = 3; b = -1; c = 4;
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, -.22, -.21}, WorkingPrecision -> 110]
RealDigits[r]   (* A200227 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
RealDigits[r]   (* A200228 *)

PARI

a=3; b=-1; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 30 2018