A197418 Decimal expansion of least x > 0 having sin(Pi*x/6) = sin(2*x/3)^2.

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

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=1.4959095464399948574965751863169680911...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = Pi/6; c = 2/3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.49, 1.5}, WorkingPrecision -> 200]
RealDigits[t] (* A197418 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 3}]
RealDigits[x/.FindRoot[Sin[Pi x/6]==Sin[2 x/3]^2,{x,1},WorkingPrecision->120],10,120][[1]] (* Harvey P. Dale, Dec 27 2024 *)