A197383 Decimal expansion of least x > 0 having sin(Pi*x/6) = sin(Pi*x/3)^2.

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

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=0.5213378295717156986919885644549179773091813947336...
		

Crossrefs

Cf. A197133, A197521.

Programs

Mathematica

b = Pi/6; c = Pi/3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .4, .6}, WorkingPrecision -> 200]
RealDigits[t] (* A197383 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2.2}]
RealDigits[ (6*ArcSec[ Root[ 16 - 16#^2 + #^6 & , 3]])/Pi, 10, 99] // First (* Jean-François Alcover, Feb 19 2013 *)