A199732 Decimal expansion of greatest x satisfying x^2-4*x*cos(x)=4*sin(x).

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

Offset

1,2

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: -3.80284270062359171640437975188554983520...
greatest:  1.71776170155914673794654693768308401...

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, -2 Pi, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3.9, -3.8}, WorkingPrecision -> 110]
RealDigits[r]   (* A199731 least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 1.71, 1.72}, WorkingPrecision -> 110]
RealDigits[r]   (* A199732 greatest of 4 roots *)

Crossrefs

Cf. A199597.

Sequence in context: A295872 A351835 A010772 * A293238 A210708 A210529

Adjacent sequences: A199729 A199730 A199731 * A199733 A199734 A199735

Keyword

nonn,cons

Author

Clark Kimberling, Nov 09 2011

Status

approved