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A195704 Decimal expansion of arccos(-sqrt(1/8)).

%I A195704 #15 Nov 21 2024 07:53:42
%S A195704 1,9,3,2,1,6,3,4,5,0,7,0,1,6,0,4,4,2,4,8,2,0,5,1,0,3,6,7,9,6,0,4,1,8,
%T A195704 1,2,3,1,1,1,1,9,3,9,4,2,8,9,9,7,7,3,0,4,4,3,0,0,8,4,9,3,6,2,4,4,5,7,
%U A195704 6,1,8,9,4,1,0,0,4,1,9,6,3,1,7,9,6,4,3,1,2,1,8,1,4,0,6,0,9,1,8,5
%N A195704 Decimal expansion of arccos(-sqrt(1/8)).
%H A195704 G. C. Greubel, <a href="/A195704/b195704.txt">Table of n, a(n) for n = 1..5000</a>
%H A195704 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A195704 Equals Pi - arcsin(sqrt(7/2)/2) = Pi - arctan(sqrt(7)). - _Amiram Eldar_, Jul 09 2023
%e A195704 arccos(-sqrt(1/8)) = 1.93216345070...
%t A195704 r = Sqrt[1/8];
%t A195704 N[ArcSin[r], 100]
%t A195704 RealDigits[%]  (* A195699 *)
%t A195704 N[ArcCos[r], 100]
%t A195704 RealDigits[%]  (* A168229 *)
%t A195704 N[ArcTan[r], 100]
%t A195704 RealDigits[%]  (* A188615 *)
%t A195704 N[ArcCos[-r], 100]
%t A195704 RealDigits[%]  (* A195704 *)
%o A195704 (PARI) acos(-sqrt(1/8)) \\ _G. C. Greubel_, Nov 18 2017
%o A195704 (Magma) [Arccos(-Sqrt(1/8))]; // _G. C. Greubel_, Nov 18 2017
%Y A195704 Cf. A195699.
%K A195704 nonn,cons
%O A195704 1,2
%A A195704 _Clark Kimberling_, Sep 23 2011