A200297 Decimal expansion of least x satisfying 4*x^2-3*cos(x)=2*sin(x).

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

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: -0.58847086928685261649979864856036...
greatest x: 0.922697336548314794603906551791...

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 *)

Prog

(PARI) a=4; b=-3; c=2; solve(x=-.59, -.58, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018

Crossrefs

Cf. A199949.

Sequence in context: A007450 A303816 A342647 * A155735 A153611 A068470

Adjacent sequences: A200294 A200295 A200296 * A200298 A200299 A200300

Keyword

nonn,cons

Author

Clark Kimberling, Nov 15 2011

Status

approved