A197291 Decimal expansion of least x>0 having sin(6x) = sin(2x)^2.

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

Offset: 0

Author

Clark Kimberling, Oct 13 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.

Least positive solution of cos x - sin x = 1/2. - Clark Kimberling, May 28 2024

Least positive solution of sin(2x) = 3/4. - Alexandru Petrescu, Jul 10 2024

Examples

			0.4240310394907405040264721694992090400...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A197260, A197133.

Programs

Mathematica

b = 6; c = 2; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .4, .6}, WorkingPrecision -> 100]
RealDigits[t] (* A197291 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]
RealDigits[ ArcTan[ (4-Sqrt[7])/3 ], 10, 100] // First (* Jean-François Alcover, Feb 27 2013 *)