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A195710 Decimal expansion of arccos(-sqrt(2/5)).

%I A195710 #17 Nov 21 2024 07:52:50
%S A195710 2,2,5,5,5,1,5,5,2,9,7,9,7,1,7,9,5,3,3,1,1,9,4,1,9,7,6,1,3,5,0,8,1,5,
%T A195710 4,5,8,0,2,7,8,5,8,0,0,8,8,3,0,2,1,5,1,7,2,6,0,2,5,8,2,8,2,2,5,0,3,0,
%U A195710 5,7,6,1,7,4,0,0,2,3,0,8,2,3,7,8,3,1,0,3,6,5,3,9,6,1,3,8,7,8,3,2
%N A195710 Decimal expansion of arccos(-sqrt(2/5)).
%H A195710 G. C. Greubel, <a href="/A195710/b195710.txt">Table of n, a(n) for n = 1..5000</a>
%H A195710 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A195710 Equals Pi - arcsin(sqrt(3/5)) = Pi - arctan(sqrt(3/2)). - _Amiram Eldar_, Jul 08 2023
%e A195710 arccos(-sqrt(2/5)) = 2.25551552979717...
%t A195710 r = Sqrt[1/5]; s = Sqrt[2/5];
%t A195710 N[ArcSin[r], 100]
%t A195710 RealDigits[%]  (* A073000 *)
%t A195710 N[ArcCos[r], 100]
%t A195710 RealDigits[%]  (* A105199 *)
%t A195710 N[ArcTan[r], 100]
%t A195710 RealDigits[%]  (* A188595 *)
%t A195710 N[ArcCos[-r], 100]
%t A195710 RealDigits[%]  (* A137218 *)
%t A195710 N[ArcSin[s], 100]
%t A195710 RealDigits[%]  (* A195701 *)
%t A195710 N[ArcCos[s], 100]
%t A195710 RealDigits[%]  (* A195708 *)
%t A195710 N[ArcTan[s], 100]
%t A195710 RealDigits[%]  (* A195709 *)
%t A195710 N[ArcCos[-s], 100]
%t A195710 RealDigits[%]  (* A195710 *)
%t A195710 RealDigits[ArcCos[-Sqrt[(2/5)]],10,120][[1]] (* _Harvey P. Dale_, Apr 06 2023 *)
%o A195710 (PARI) acos(-sqrt(2/5)) \\ _G. C. Greubel_, Nov 18 2017
%o A195710 (Magma) [Arccos(-Sqrt(2/5))]; // _G. C. Greubel_, Nov 18 2017
%Y A195710 Cf. A195708, A195701.
%K A195710 nonn,cons
%O A195710 1,1
%A A195710 _Clark Kimberling_, Sep 23 2011