A200127 Decimal expansion of greatest x satisfying 2*x^2 - 3*cos(x) = 4*sin(x).

1, 4, 6, 5, 2, 3, 5, 3, 8, 6, 1, 4, 2, 6, 3, 1, 8, 5, 6, 9, 4, 5, 9, 2, 6, 8, 3, 0, 5, 7, 2, 6, 9, 4, 9, 2, 6, 9, 0, 0, 7, 8, 8, 8, 6, 2, 5, 1, 9, 6, 6, 4, 6, 8, 7, 8, 7, 8, 3, 9, 7, 1, 6, 8, 3, 1, 4, 1, 7, 3, 5, 2, 9, 3, 5, 6, 5, 7, 7, 2, 4, 5, 6, 1, 7, 8, 8, 7, 7, 2, 4, 7, 3, 1, 0, 3, 9, 9, 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: -0.530633047496848880166804175671064100...
greatest x: 1.4652353861426318569459268305726949...

Mathematica

a = 2; 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, -.54, -.53}, WorkingPrecision -> 110]
RealDigits[r]  (* A200126 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.46, 1.47}, WorkingPrecision -> 110]
RealDigits[r]  (* A200127 *)

Prog

(PARI) a=2; b=-3; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 01 2018

Crossrefs

Cf. A199949.

Sequence in context: A019123 A308716 A021219 * A222069 A274318 A256682

Adjacent sequences: A200124 A200125 A200126 * A200128 A200129 A200130

Keyword

nonn,cons

Author

Clark Kimberling, Nov 14 2011

Status

approved