A200282 Decimal expansion of greatest x satisfying 3*x^2 - 4*cos(x) = 3*sin(x).

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

Offset

1,3

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 = 1..10000

Example

least x: -0.6615723781879899920628993073289...
greatest x: 1.19240455007681565929009549661...

Mathematica

a = 3; b = -4; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.67, -.66}, WorkingPrecision -> 110]
RealDigits[r]    (* A200281 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
RealDigits[r]   (* A200282 *)

Prog

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

Crossrefs

Cf. A199949.

Sequence in context: A248322 A248321 A248320 * A133841 A099769 A176517

Adjacent sequences: A200279 A200280 A200281 * A200283 A200284 A200285

Keyword

nonn,cons

Author

Clark Kimberling, Nov 15 2011

Status

approved