A200306 Decimal expansion of greatest x satisfying 4*x^2 - 4*cos(x) = sin(x).

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

Offset: 0

Author

Clark Kimberling, Nov 16 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least x: -0.749483556259155223568363487735793...
greatest x: 0.9030596139048642509102274645526...
		

Links

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

Crossrefs

Cf. A199949.

Programs

Mathematica

a = 4; b = -4; c = 1;
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, -.75, -.74}, WorkingPrecision -> 110]
RealDigits[r]   (* A200305 *)
r = x /. FindRoot[f[x] == g[x], {x, .90, .91}, WorkingPrecision -> 110]
RealDigits[r]    (* A200306 *)

PARI

a=4; b=-4; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 08 2018