A200286 Decimal expansion of least x satisfying 4*x^2 - cos(x) = sin(x).

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

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: -0.37540364996113984869295773583715442...
greatest x: 0.588851742675041179999659714644848...

Mathematica

a = 4; b = -1; c = 1;
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, -.38, -.37}, WorkingPrecision -> 110]
RealDigits[r]   (* A200285 *)
r = x /. FindRoot[f[x] == g[x], {x, .58, .59}, WorkingPrecision -> 110]
RealDigits[r]   (* A200286 *)

Prog

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

Crossrefs

Cf. A199949.

Sequence in context: A247037 A265274 A365523 * A073822 A198606 A031165

Adjacent sequences: A200283 A200284 A200285 * A200287 A200288 A200289

Keyword

nonn,cons

Author

Clark Kimberling, Nov 15 2011

Status

approved