A200133 Decimal expansion of greatest x satisfying 3*x^2 - cos(x) = sin(x).

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

Offset

0,1

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 = 0..10000

Example

least x: -0.4137517591447739376844002798989...
greatest x: 0.684853078623201159563694468649...

Mathematica

a = 3; b = -1; c = 1;
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, -.42, -.41}, WorkingPrecision -> 110]
RealDigits[r]   (* A200132 *)
r = x /. FindRoot[f[x] == g[x], {x, .68, .69}, WorkingPrecision -> 110]
RealDigits[r]   (* A200133 *)

Prog

(PARI) a=3; b=-1; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 05 2018

Crossrefs

Cf. A199949.

Sequence in context: A269802 A269991 A171784 * A021150 A347407 A065166

Adjacent sequences: A200130 A200131 A200132 * A200134 A200135 A200136

Keyword

nonn,cons

Author

Clark Kimberling, Nov 14 2011

Status

approved