%I
%S 8,4,8,0,6,2,0,7,8,9,8,1,4,8,1,0,0,8,0,5,2,9,4,4,3,3,8,9,9,8,4,1,8,0,
%T 8,0,0,7,3,3,6,6,2,1,3,2,6,3,1,1,2,6,4,2,8,6,0,7,1,8,1,6,3,5,7,0,2,0,
%U 0,8,2,1,2,2,8,4,7,4,2,3,4,3,4,9,1,8,9,8,0,1,7,3,1,9,5,7,2,3,0,3
%N Decimal expansion of least x>0 having sin(3x)=(sin x)^2.
%C 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.
%e x=0.8480620789814810080529443389984180800...
%t b = 3; c = 1; f[x_] := Sin[x]
%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .6, 1}, WorkingPrecision > 100]
%t RealDigits[t] (* A197260 *)
%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]
%t RealDigits[ ArcCos[ Sqrt[7]/4], 10, 100] // First (* _JeanFrançois Alcover_, Feb 19 2013 *)
%Y Cf. A197133.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 12 2011
