A197292 Decimal expansion of least x>0 having sin(6x)=(sin 3x)^2.

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

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.

Examples

			x=0.3690495725980301676723551533928456800...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = 6; c = 3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .3, .4}, WorkingPrecision -> 100]
RealDigits[t] (* A197292 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]
RealDigits[ ArcCos[ Sqrt[ Root[-1 + 45# - 120#^2 + 80#^3 & , 3]]], 10, 100] // First (* Jean-François Alcover, Feb 19 2013 *)