A199775 Decimal expansion of x>0 satisfying 2*x^2 - 2*x*cos(x) = 3*sin(x).

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

Offset: 1

Author

Clark Kimberling, Nov 10 2011

Keywords

• nonn
• cons

Comments

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

Examples

			1.331486959335040503327363069917339543025...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 2; b = -2; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.33, 1.34}, WorkingPrecision -> 110]
RealDigits[r]   (* A199775 *)
RealDigits[x/.FindRoot[2 x^2-2 x Cos[x]==3 Sin[x],{x,1.3},WorkingPrecision->120],10,120][[1]] (* Harvey P. Dale, Jul 06 2025 *)

PARI

solve(x=1,2,2*x^2-2*x*cos(x)-3*sin(x)) \\ Charles R Greathouse IV, Dec 28 2011