A199607 Decimal expansion of least x satisfying x^2+3*x*cos(x)=2*sin(x).

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

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: -0.5973392503648539750049736135997669028331...
greatest:  3.0481385953651166891446050593739052208...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A199597.

Programs

Mathematica

a = 1; b = 3; c = 2;
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, -.6, -.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199607, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3, 3.1}, WorkingPrecision -> 110]
RealDigits[r]  (* A199708, greatest of 4 roots *)