A199617 Decimal expansion of least x satisfying x^2+4*x*cos(x)=3*sin(x).

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

Offset: 0

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: -0.5535433817860336287020344905911816930...
greatest:  3.4822676247861932090867036675576803...
		

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, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.56, -.55}, WorkingPrecision -> 110]
RealDigits[r]  (* A199617, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199618, greatest of 4 roots *)