A197260 Decimal expansion of least x>0 having sin(3x) = sin(x)^2.

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

Offset: 0

Author

Clark Kimberling, Oct 12 2011

Keywords

• nonn
• cons

Comments

The Mathematica program includes a graph. See A197133 for a guide to least x>0 satisfying sin(b*x)=(sin(c*x))^2 for selected b and c.

Examples

			0.84806207898148100805294433899841808007...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A197291, A197133, A197377.

Programs

Mathematica

b = 3; c = 1; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .6, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* this sequence *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]
RealDigits[ ArcCos[ Sqrt[7]/4], 10, 100] // First (* Jean-François Alcover, Feb 19 2013 *)

Formula

Equals arcsin(3/4). - Alexandru Petrescu, Jul 08 2024

Equals 2*A197291 = A197377/3. - Hugo Pfoertner, Jul 08 2024