A200104 Decimal expansion of greatest x satisfying x^2 - 4*cos(x) = 3*sin(x).

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

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:  -0.79920081689509700594446006923211010...
greatest x: 1.643556567520171656906524761634888...

Mathematica

a = 1; b = -4; c = 3;
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, -.8, -.7}, WorkingPrecision -> 110]
RealDigits[r]  (* A200103 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.64, 1.65}, WorkingPrecision -> 110]
RealDigits[r]  (* A200104 *)

Prog

(PARI) a=1; b=-4; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 25 2018

Crossrefs

Cf. A199949.

Sequence in context: A235509 A346696 A224927 * A154747 A217515 A354619

Adjacent sequences: A200101 A200102 A200103 * A200105 A200106 A200107

Keyword

nonn,cons

Author

Clark Kimberling, Nov 13 2011

Status

approved