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Decimal expansion of 3*Pi/(4+Pi).
2

%I #10 Oct 01 2022 00:54:38

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

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

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

%N Decimal expansion of 3*Pi/(4+Pi).

%C Least x>0 such that sin(bx)=cos(cx) (and also sin(cx)=cos(bx)), where b=2/3 and c=Pi/6; 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 1.3197025394653278722685641235411401513975623...

%t b = 2/3; c = Pi/6;

%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.131, 1.132}]

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

%t RealDigits[%] (* A197730 *)

%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 1,2

%A _Clark Kimberling_, Oct 17 2011