A200098 Decimal expansion of greatest x satisfying x^2 - 3*cos(x) = 4*sin(x).

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

Offset

1,2

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:  -0.576891176962186435752436597718261688130...
greatest x: 1.79646741863500842707885236614949093773...

Mathematica

a = 1; b = -3; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.58, -.57}, WorkingPrecision -> 110]
RealDigits[r]  (* A200097 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.79, 1.80}, WorkingPrecision -> 110]
RealDigits[r]  (* A200098 *)

Prog

(PARI) a=1; b=-3; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 24 2018

Crossrefs

Cf. A199949.

Sequence in context: A099877 A197327 A199471 * A239069 A154168 A019644

Adjacent sequences: A200095 A200096 A200097 * A200099 A200100 A200101

Keyword

nonn,cons

Author

Clark Kimberling, Nov 13 2011

Status

approved