A199734 Decimal expansion of greatest x satisfying x^2-4*x*cos(x)=3*sin(x).

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

Offset: 1

Author

Clark Kimberling, Nov 09 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least: -3.746168565528221340687013560527596978856...
greatest:  1.625278383378448643933003226246836106...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 1; b = -4; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -4, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3.8, -3.7}, WorkingPrecision -> 110]
RealDigits[r]   (* A199733 least root *)
r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
RealDigits[r]   (* A199734 greatest root *)