A197416 Decimal expansion of least x > 0 having sin(Pi*x/6) = sin(x/2)^2.

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

Offset: 1

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=3.08135000586802502176095647904...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = Pi/6; c = 1/2; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 3, 3.1}, WorkingPrecision -> 200]
RealDigits[t] (* A197416 *)
Plot[{f[b*x], f[c*x]^2}, {x, 3, 3.8}]