A200298 Decimal expansion of greatest x satisfying 4*x^2-3*cos(x)=2*sin(x).

9, 2, 2, 6, 9, 7, 3, 3, 6, 5, 4, 8, 3, 1, 4, 7, 9, 4, 6, 0, 3, 9, 0, 6, 5, 5, 1, 7, 9, 1, 5, 6, 2, 3, 6, 8, 8, 9, 4, 9, 0, 9, 0, 4, 9, 0, 7, 7, 2, 5, 7, 0, 5, 8, 6, 7, 3, 2, 2, 9, 0, 3, 3, 1, 1, 2, 1, 4, 2, 4, 9, 0, 9, 0, 3, 3, 9, 7, 3, 4, 8, 4, 2, 3, 0, 2, 3, 5, 1, 4, 5, 3, 8, 5, 5, 6, 8, 7, 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: -0.58847086928685261649979864856036...
greatest x: 0.922697336548314794603906551791...
		

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 = -3; c = 2;
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, -.59, -.58}, WorkingPrecision -> 110]
RealDigits[r]   (* A200297 *)
r = x /. FindRoot[f[x] == g[x], {x, .92, .93}, WorkingPrecision -> 110]
RealDigits[r]   (* A200298 *)

PARI

a=4; b=-3; c=2; solve(x=.92, .93, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018