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A196772 Decimal expansion of the number c for which the curve y=1/x is tangent to the curve y=sin(x-c), and 0<x<2 pi; c=pi-sqrt(r)-arccos(r-1), where r=(1+sqrt(5))/2 (the golden ratio). 7

%I

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

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

%U 9,6,1,6,9,8,6,0,9,5,7,6,9,1,9,1,5,4,0,0,2,8,8,5,2,1,7,9,4,1,0,7

%N Decimal expansion of the number c for which the curve y=1/x is tangent to the curve y=sin(x-c), and 0<x<2 pi; c=pi-sqrt(r)-arccos(r-1), where r=(1+sqrt(5))/2 (the golden ratio).

%e c=0.965016109773342910082904125880052671050...

%t Plot[{Sin[x + .97], 1/x}, {x, 0, Pi}]

%t r = GoldenRatio; x = Sqrt[r];

%t c = N[Pi - x - ArcCos[r - 1], 100]

%t RealDigits[c] (* A196772 *)

%t slope = N[-1/x^2, 100]

%t RealDigits[slope] (* 1-r *)

%Y Cf. A195625, A196767.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 06 2011

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Last modified October 23 12:19 EDT 2019. Contains 328345 sequences. (Running on oeis4.)