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A195708 Decimal expansion of arccos(sqrt(2/5)) and of arcsin(sqrt(3/5)).

%I A195708 #15 Nov 21 2024 07:42:34
%S A195708 8,8,6,0,7,7,1,2,3,7,9,2,6,1,3,7,0,5,3,4,3,2,2,3,6,2,1,9,2,8,6,8,7,4,
%T A195708 2,6,1,6,9,3,1,1,3,9,0,5,4,4,8,9,0,6,4,8,3,7,2,3,6,1,7,6,9,8,0,4,7,5,
%U A195708 8,7,8,8,8,8,5,9,7,8,1,7,4,8,4,4,9,3,1,1,7,1,3,8,0,7,2,9,2,3,5,4
%N A195708 Decimal expansion of arccos(sqrt(2/5)) and of arcsin(sqrt(3/5)).
%H A195708 G. C. Greubel, <a href="/A195708/b195708.txt">Table of n, a(n) for n = 0..5000</a>
%H A195708 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A195708 Equals arctan(sqrt(3/2)). - _Amiram Eldar_, Jul 04 2023
%e A195708 0.886077123792...
%t A195708 r = Sqrt[1/5]; s = Sqrt[2/5];
%t A195708 N[ArcSin[r], 100]
%t A195708 RealDigits[%]  (* A073000 *)
%t A195708 N[ArcCos[r], 100]
%t A195708 RealDigits[%]  (* A105199 *)
%t A195708 N[ArcTan[r], 100]
%t A195708 RealDigits[%]  (* A188595 *)
%t A195708 N[ArcCos[-r], 100]
%t A195708 RealDigits[%]  (* A137218 *)
%t A195708 N[ArcSin[s], 100]
%t A195708 RealDigits[%]  (* A195701 *)
%t A195708 N[ArcCos[s], 100]
%t A195708 RealDigits[%]  (* A195708 *)
%t A195708 N[ArcTan[s], 100]
%t A195708 RealDigits[%]  (* A195709 *)
%t A195708 N[ArcCos[-s], 100]
%t A195708 RealDigits[%]  (* A195710 *)
%o A195708 (PARI) acos(sqrt(2/5)) \\ _G. C. Greubel_, Nov 18 2017
%o A195708 (Magma) [Arccos(Sqrt(2/5))]; // _G. C. Greubel_, Nov 18 2017
%Y A195708 Cf. A073000, A105199, A195701.
%K A195708 nonn,cons
%O A195708 0,1
%A A195708 _Clark Kimberling_, Sep 23 2011