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Decimal expansion of least x>0 having sin(4x)=(sin 3x)^2.
2

%I #8 Jan 22 2013 08:37:43

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

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

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

%N Decimal expansion of least x>0 having sin(4x)=(sin 3x)^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=0.4599755354050940320651507516304768327270591...

%t b = 4; c = 3; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .4, .5}, WorkingPrecision -> 100]

%t RealDigits[t] (* A197268 *)

%t Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]

%Y Cf. A197133.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 12 2011