A200005 Decimal expansion of greatest x satisfying 2*x^2 + cos(x) = 4*sin(x).

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

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:  0.2841554251771481491680536288735443310...
greatest x: 1.36083225539066890467183928569132636...
		

Links

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

Crossrefs

Cf. A199949.

Programs

Mathematica

a = 2; b = 1; c = 4;
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, .28, .29}, WorkingPrecision -> 110]
RealDigits[r]   (* A200004 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.4}, WorkingPrecision -> 110]
RealDigits[r]   (* A200005 *)

PARI

a=2; b=1; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018