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A195709 Decimal expansion of arctan(sqrt(2/5)).

%I A195709 #11 Nov 20 2024 23:41:34
%S A195709 5,6,3,9,4,2,6,4,1,3,6,0,6,2,8,8,4,2,6,9,3,8,3,1,1,7,2,1,8,3,7,4,6,8,
%T A195709 4,7,8,5,1,8,5,9,5,3,9,3,0,4,2,5,6,7,8,3,7,5,7,2,4,2,6,6,4,2,6,6,9,2,
%U A195709 6,2,7,9,6,5,7,8,7,4,1,2,3,6,4,0,9,2,9,4,5,7,1,8,8,3,8,4,5,1,4,2
%N A195709 Decimal expansion of arctan(sqrt(2/5)).
%H A195709 G. C. Greubel, <a href="/A195709/b195709.txt">Table of n, a(n) for n = 0..5000</a>
%H A195709 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A195709 arctan(sqrt(2/5)) = 0.5639426413606...
%t A195709 r = Sqrt[1/5]; s = Sqrt[2/5];
%t A195709 N[ArcSin[r], 100]
%t A195709 RealDigits[%]  (* A073000 *)
%t A195709 N[ArcCos[r], 100]
%t A195709 RealDigits[%]  (* A105199 *)
%t A195709 N[ArcTan[r], 100]
%t A195709 RealDigits[%]  (* A188595 *)
%t A195709 N[ArcCos[-r], 100]
%t A195709 RealDigits[%]  (* A137218 *)
%t A195709 N[ArcSin[s], 100]
%t A195709 RealDigits[%]  (* A195701 *)
%t A195709 N[ArcCos[s], 100]
%t A195709 RealDigits[%]  (* A195708 *)
%t A195709 N[ArcTan[s], 100]
%t A195709 RealDigits[%]  (* A195709 *)
%t A195709 N[ArcCos[-s], 100]
%t A195709 RealDigits[%]  (* A195710 *)
%o A195709 (PARI) atan(sqrt(2/5)) \\ _G. C. Greubel_, Nov 18 2017
%o A195709 (Magma) [Arctan(Sqrt(2/5))]; // _G. C. Greubel_, Nov 18 2017
%Y A195709 Cf. A195708.
%K A195709 nonn,cons
%O A195709 0,1
%A A195709 _Clark Kimberling_, Sep 23 2011