A199957 Decimal expansion of least x satisfying x^2 + 2*cos(x) = 4*sin(x).

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

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:  0.525416279282353649071522053392...
greatest x: 2.1115948673130941666464133109...

Mathematica

a = 1; b = 2; 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, .52, .53}, WorkingPrecision -> 110]
RealDigits[r]   (* A199957 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.1, 2.2}, WorkingPrecision -> 110]
RealDigits[r]  (* A199958 *)

Prog

(PARI) a=1; b=2; c=4; solve(x=.5, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018

Crossrefs

Cf. A199949.

Sequence in context: A278066 A153107 A247488 * A020855 A007292 A191583

Adjacent sequences: A199954 A199955 A199956 * A199958 A199959 A199960

Keyword

nonn,cons

Author

Clark Kimberling, Nov 12 2011

Status

approved