A199954 Decimal expansion of greatest x satisfying x^2+cos(x)=4*sin(x).

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

Offset: 1

Author

Clark Kimberling, Nov 12 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least x:  0.26157393647481130212296420178312116039782...
greatest x: 2.011137342229330846002506540879639388630...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A199949.

Programs

Mathematica

a = 1; b = 1; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .26, .27}, WorkingPrecision -> 110]
RealDigits[r]  (* A199953 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.0, 2.1}, WorkingPrecision -> 110]
RealDigits[r]  (* A199954 *)

PARI

a=1; b=1; c=4; solve(x=2, 2.1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018