A200015 Decimal expansion of greatest x satisfying x^2 - cos(x) = 3*sin(x).

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

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:  -0.2943487723356863983696578902036195...
greatest x: 1.690779738969815334957504857558809...

Mathematica

a = 1; b = -1; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.3, -.29}, WorkingPrecision -> 110]
RealDigits[r]  (* A200014 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
RealDigits[r]   (* A200015 *)

Prog

(PARI) a=1; b=-1; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

Crossrefs

Cf. A199949.

Sequence in context: A020792 A242760 A196607 * A298517 A199451 A135154

Adjacent sequences: A200012 A200013 A200014 * A200016 A200017 A200018

Keyword

nonn,cons

Author

Clark Kimberling, Nov 12 2011

Extensions

a(88)-a(99) corrected by G. C. Greubel, Jun 23 2018

Status

approved