A200290 Decimal expansion of greatest x satisfying 4*x^2 - cos(x) = 3*sin(x).

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

Offset: 0

Author

Clark Kimberling, Nov 15 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least x: -0.2454630318308242424706176604707384581...
greatest x: 0.85425847729971214786694703263536193...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A199949.

Programs

Mathematica

a = 4; b = -1; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.25, -.24}, WorkingPrecision -> 110]
RealDigits[r]    (* A200289 *)
r = x /. FindRoot[f[x] == g[x], {x, .85, .86}, WorkingPrecision -> 110]
RealDigits[r]    (* A200290 *)

PARI

a=4; b=-1; c=3; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 07 2018