A199965 Decimal expansion of least x satisfying x^2 + 4*cos(x) = 4*sin(x).

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

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:  0.943379571591794622084167020515639838...
greatest x: 2.3781281686737679859682016614728862...

Mathematica

a = 1; b = 4; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .94, .95}, WorkingPrecision -> 110]
RealDigits[r]  (* A199965 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.37, 2.38}, WorkingPrecision -> 110]
RealDigits[r]  (* A199966 *)

Prog

(PARI) a=1; b=4; c=4; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

Crossrefs

Cf. A199949.

Sequence in context: A033329 A097326 A282100 * A021110 A010540 A187466

Adjacent sequences: A199962 A199963 A199964 * A199966 A199967 A199968

Keyword

nonn,cons

Author

Clark Kimberling, Nov 12 2011

Status

approved