A200239 Decimal expansion of least x satisfying 3*x^2-3*cos(x)=2*sin(x).

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

Offset: 0

Author

Clark Kimberling, Nov 15 2011

Keywords

• nonn
• cons

Comments

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least x: -0.63766115794607313411989545658819620...
greatest x: 1.039829693324607596071793532120387...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A199949.

Programs

Mathematica

a = 3; b = -3; c = 2;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.64, -.63}, WorkingPrecision -> 110]
RealDigits[r]   (* A200239 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A200240 *)

PARI

a=3; b=-3; c=2; solve(x=-.64, -.63, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018