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Decimal expansion of arctan(sqrt(3/8)).
3

%I #15 Nov 20 2024 23:41:08

%S 5,4,9,4,6,7,2,4,4,7,5,7,6,2,7,3,7,1,0,8,5,4,0,0,2,5,0,3,2,6,7,3,1,9,

%T 7,6,9,9,3,0,6,1,4,2,4,2,5,6,8,9,1,9,0,6,8,2,3,2,2,4,8,1,3,3,3,3,9,9,

%U 8,2,8,1,3,9,4,6,6,3,7,0,7,8,4,3,0,0,0,9,9,9,7,3,0,0,6,2,1,6,0,2

%N Decimal expansion of arctan(sqrt(3/8)).

%H G. C. Greubel, <a href="/A195705/b195705.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals arcsin(sqrt(3/11)) = arccos(2*sqrt(2/11)). - _Amiram Eldar_, Jul 09 2023

%e arctan(sqrt(3/8)) = 0.549467244757...

%t r = Sqrt[3/8];

%t N[ArcSin[r], 100]

%t RealDigits[%] (* A195700 *)

%t N[ArcCos[r], 100]

%t RealDigits[%] (* A195703 *)

%t N[ArcTan[r], 100]

%t RealDigits[%] (* A195705 *)

%t N[ArcCos[-r], 100]

%t RealDigits[%] (* A195706 *)

%o (PARI) atan(sqrt(3/8)) \\ _G. C. Greubel_, Nov 18 2017

%o (Magma) [Arctan(Sqrt(3/8))]; // _G. C. Greubel_, Nov 18 2017

%Y Cf. A195700.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Sep 23 2011