cp's OEIS Frontend

A335957 Decimal expansion of s/c, where s = arclength on y = sin(x) from (0,0) to (Pi/4,sqrt(1/2)), and c = arclength on y = cos(x) from (0,1) to (Pi/4,sqrt(1/2)).

%I A335957 #5 Jul 04 2020 01:45:23
%S A335957 1,2,4,1,8,9,1,1,8,2,5,1,7,7,7,9,4,9,3,2,8,0,2,9,7,4,2,6,7,0,3,6,9,2,
%T A335957 3,6,5,2,9,6,2,9,4,7,6,4,2,5,6,1,6,6,2,1,3,8,6,4,8,0,3,3,4,7,0,3,7,1,
%U A335957 8,8,4,7,4,9,7,8,7,6,5,8,2,8,2,5,8,0
%N A335957 Decimal expansion of s/c, where s = arclength on y = sin(x) from (0,0) to (Pi/4,sqrt(1/2)), and c = arclength on y = cos(x) from (0,1) to (Pi/4,sqrt(1/2)).
%e A335957 s/c = 1.24189118251777949328029742670369236529...
%e A335957 c/s = 0.80522352849999684548520974994993752239...
%e A335957 c-s = 0.20609210827127010650339774278617212954...
%t A335957 r1 = NIntegrate[Sqrt[1 + Cos[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
%t A335957 r2 = NIntegrate[Sqrt[1 + Sin[t]^2], {t, 0, Pi/4}, WorkingPrecision -> 200]
%t A335957 r1/r2
%t A335957 r2/r1
%t A335957 r1 - r2
%t A335957 RealDigits[r1/r2][[1]]      (* A335957 *)
%t A335957 RealDigits[r2/r1][[1]]      (* A335958 *)
%t A335957 RealDigits[r1 - r2][[1]]    (* A335959 *)
%Y A335957 Cf. A335928, A335929, A335930, A335931, A335932, A335958, A335959.
%K A335957 nonn,cons
%O A335957 1,2
%A A335957 _Clark Kimberling_, Jul 03 2020