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

Author

Clark Kimberling, Nov 12 2011

Keywords

• nonn
• cons

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A199949.

Programs

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 *)

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