A199620 Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=4*sin(x).

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

Offset

1,1

Comments

See A199597 for a guide to related sequences. The Mathematica program includes a graph.

Links

Table of n, a(n) for n=1..99.

Example

least: 0.80005334262741575936859027990893321963...
greatest:  3.4528998885329277803363008378649838...

Mathematica

a = 1; b = 4; c = 4;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -.5, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .8, .81}, WorkingPrecision -> 110]
RealDigits[r]  (* A199619, least pos root *)
r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199620, greatest of 3 roots *)

Crossrefs

Cf. A199597.

Sequence in context: A280488 A250072 A099120 * A016553 A228947 A337535

Adjacent sequences: A199617 A199618 A199619 * A199621 A199622 A199623

Keyword

nonn,cons

Author

Clark Kimberling, Nov 08 2011

Status

approved