A199610 Decimal expansion of greatest x satisfying x^2+3*x*cos(x)=3*sin(x).

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

Offset: 1

Author

Clark Kimberling, Nov 08 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least: 1.14225640224474011004461587823586435251534483...
greatest:  3.0656207603368585618674575528508213250654...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 1; b = 3; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
RealDigits[r]  (* A199609, least of 3 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3, 3.1}, WorkingPrecision -> 110]
RealDigits[r]  (* A199610, greatest of 3 roots *)