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A195701 Decimal expansion of arctan(sqrt(2/3)).

%I A195701 #15 Nov 20 2024 23:40:01
%S A195701 6,8,4,7,1,9,2,0,3,0,0,2,2,8,2,9,1,3,8,8,8,0,9,8,0,6,9,7,1,1,0,6,4,0,
%T A195701 1,5,9,2,9,2,7,3,3,0,9,1,4,2,6,6,2,2,6,2,1,1,5,1,1,0,5,2,6,3,4,9,1,4,
%U A195701 9,4,1,4,2,5,7,1,2,6,3,2,4,4,6,9,0,8,6,2,4,1,2,9,0,3,2,9,2,9,8,5
%N A195701 Decimal expansion of arctan(sqrt(2/3)).
%H A195701 G. C. Greubel, <a href="/A195701/b195701.txt">Table of n, a(n) for n = 0..5000</a>
%H A195701 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A195701 Equals arcsin(sqrt(2/5)) = arccos(sqrt(3/5)). - _Amiram Eldar_, Jul 10 2023
%e A195701 arctan(sqrt(2/3)) = 0.68471920300...
%t A195701 r = Sqrt[2/3];
%t A195701 N[ArcSin[r], 100]
%t A195701 RealDigits[%]  (* A195696 *)
%t A195701 N[ArcCos[r], 100]
%t A195701 RealDigits[%]  (* A195695 *)
%t A195701 N[ArcTan[r], 100]
%t A195701 RealDigits[%]  (* A195701 *)
%t A195701 N[ArcCos[-r], 100]
%t A195701 RealDigits[%]  (* A195702 *)
%o A195701 (PARI) atan(sqrt(2/3)) \\ _G. C. Greubel_, Nov 18 2017
%o A195701 (Magma) [Arctan(Sqrt(2/3))]; // _G. C. Greubel_, Nov 18 2017
%Y A195701 Cf. A195695, A195695, A195702.
%K A195701 nonn,cons
%O A195701 0,1
%A A195701 _Clark Kimberling_, Sep 23 2011