login
Decimal expansion of Pi/(4 + Pi).
2

%I #11 Oct 01 2022 00:49:37

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

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

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

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

%C Least x > 0 such that sin(b*x) = cos(c*x) (and also sin(c*x) = cos(b*x)), where b=2 and c=Pi/2; 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 0.4399008464884426240895213745137133837991874432...

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

%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .4, .45}]

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

%t RealDigits[%] (* A197694 *)

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

%t Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 1.1}]

%Y Cf. A197682.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 17 2011