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A197134 Decimal expansion of least x>0 having sin(x)=(sin 3x)^2. 2

%I #11 Feb 19 2013 05:49:39

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

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

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

%N Decimal expansion of least x>0 having sin(x)=(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=0.115402267387127882859236747957368...

%t b = 1; c = 3; f[x_] := Sin[x]

%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .1, .3}, WorkingPrecision -> 100]

%t RealDigits[t] (* A197134 *)

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

%t RealDigits[ ArcCos[ Root[ 17 - 112 #^2 + 352 #^4 - 512 #^6 + 256 #^8 &, 4]], 10, 100] // First (* _Jean-François Alcover_, Feb 19 2013 *)

%Y Cf. A197133.

%K nonn,cons

%O 0,3

%A _Clark Kimberling_, Oct 12 2011

%E Digits from a(79) on corrected by _Jean-François Alcover_, Feb 19 2013

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Last modified March 29 05:43 EDT 2024. Contains 371264 sequences. (Running on oeis4.)