A199956 Decimal expansion of greatest x satisfying x^2 + 2*cos(x) = 3*sin(x).

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

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:  0.74080336819413223759642692454702162091742...
greatest x: 1.854778410356751774141939581736998761204...
		

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 = 3;
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, .74, .75}, WorkingPrecision -> 110]
RealDigits[r]  (* A199955 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.8, 1.9}, WorkingPrecision -> 110]
RealDigits[r]  (* A199956 *)

PARI

a=1; b=2; c=3; solve(x=.5, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018