A200009 Decimal expansion of greatest x satisfying 4*x^2 + cos(x) = 4*sin(x).

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

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:  0.4039548562770990578793534464221104111...
greatest x: 0.59247029079250393293128227628806324...

Mathematica

a = 4; b = 1; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, .3, .7}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .40, .41}, WorkingPrecision -> 110]
RealDigits[r]  (* A200008 *)
r = x /. FindRoot[f[x] == g[x], {x, .59, .60}, WorkingPrecision -> 110]
RealDigits[r]  (* A200009 *)

Prog

(PARI) a=4; b=1; c=4; solve(x=.5, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

Crossrefs

Cf. A199949.

Sequence in context: A323985 A198734 A332326 * A303662 A011494 A214395

Adjacent sequences: A200006 A200007 A200008 * A200010 A200011 A200012

Keyword

nonn,cons

Author

Clark Kimberling, Nov 12 2011

Status

approved