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Decimal expansion of 3*Pi/(2 + 2*Pi).
2

%I #10 Oct 01 2022 00:54:13

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

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

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

%N Decimal expansion of 3*Pi/(2 + 2*Pi).

%C Least x > 0 such that sin(b*x) = cos(c*x) (and also sin(c*x) = cos(b*x)), where b=1/3 and c=Pi/3; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 1.1378204894921642180166460335673392962076...

%t b = 1/3; c = Pi/3;

%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.137, 1.138}]

%t N[Pi/(2*b + 2*c), 110]

%t RealDigits[%] (* A197728 *)

%t Simplify[Pi/(2*b + 2*c)]

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

%Y Cf. A197682.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Oct 17 2011