A200019 Decimal expansion of greatest x satisfying x^2 - 2*cos(x) = sin(x).

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

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:  -0.8096299991295524131861096984840271321...
greatest x: 1.254187962477919553363912326321801374...
		

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 = -2; c = 1;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.9, -.8}, WorkingPrecision -> 110]
RealDigits[r]  (* A200018 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
RealDigits[r]  (* A200019 *)

PARI

a=1; b=-2; c=1; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 24 2018