A197415 Decimal expansion of least x > 0 having sin(Pi*x/6) = sin(3*x)^2.

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

Offset: 0

Author

Clark Kimberling, Oct 14 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=0.0587750562246299509776441422425948...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = Pi/6; c = 3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 0.05, 0.06},
   WorkingPrecision -> 200]
RealDigits[t] (* A197415 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.2}]