A200123 Decimal expansion of greatest x satisfying 2*x^2 - 3*cos(x) = 2*sin(x).

1, 2, 1, 0, 3, 0, 1, 1, 0, 2, 1, 5, 6, 0, 5, 7, 8, 5, 9, 1, 9, 2, 8, 4, 4, 2, 4, 6, 7, 5, 9, 4, 3, 4, 7, 8, 0, 3, 8, 1, 4, 9, 4, 7, 5, 5, 4, 4, 3, 5, 2, 6, 5, 4, 1, 2, 5, 5, 9, 4, 7, 5, 6, 4, 0, 2, 5, 1, 2, 6, 1, 3, 0, 6, 7, 4, 9, 2, 0, 3, 2, 8, 7, 4, 6, 6, 2, 1, 4, 2, 7, 4, 1, 2, 6, 4, 8, 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: -0.70415945703712255268105833349948348210...
greatest x: 1.210301102156057859192844246759434780...

Mathematica

a = 2; b = -3; c = 2;
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, -.71, -.70}, WorkingPrecision -> 110]
RealDigits[r]  (* A200122 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
RealDigits[r]  (* A200123 *)

Prog

(PARI) a=2; b=-3; c=2; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 29 2018

Crossrefs

Cf. A199949.

Sequence in context: A165252 A371954 A127373 * A187616 A217262 A378148

Adjacent sequences: A200120 A200121 A200122 * A200124 A200125 A200126

Keyword

nonn,cons

Author

Clark Kimberling, Nov 14 2011

Status

approved