cp's OEIS Frontend

A197021 Decimal expansion of the radius of the circle tangent to the curve y=cos(3x) at points (x,y) and (-x,y), where 0

%I A197021 #5 Mar 30 2012 18:57:52
%S A197021 3,7,1,8,1,1,0,4,1,7,3,6,1,7,2,1,8,4,0,1,9,5,6,4,7,3,5,1,5,8,8,5,7,9,
%T A197021 0,2,8,9,7,0,6,2,6,3,9,2,8,8,3,6,4,8,1,7,8,7,7,3,4,1,4,7,3,3,1,8,5,2,
%U A197021 8,8,2,0,5,1,3,1,2,7,3,1,4,2,0,5,9,8,0,8,0,0,1,2,2,6,8,5,7,4,2
%N A197021 Decimal expansion of the radius of the circle tangent to the curve y=cos(3x) at points (x,y) and (-x,y), where 0<x<1.
%C A197021 Let (x,y) denote the point of tangency.  Then
%C A197021 x=0.346818914654599529577486037538498433565584415464...
%C A197021 y=0.505826306518745297430716717373078359704411629139...
%C A197021 slope=-2.5879060509806840663013781941932136174746999...
%C A197021 (The Mathematica program includes a graph.)
%e A197021 radius=0.3718110417361721840195647351588579028970626...
%t A197021 r = .371; c = 3;
%t A197021 Show[Plot[Cos[c*x], {x, -0.5, 0.5}],
%t A197021  ContourPlot[x^2 + (y - r)^2 == r^2, {x, -1, 1}, {y, -1, 1}], PlotRange -> All, AspectRatio -> Automatic]
%t A197021 t = x /. FindRoot[c*Sin[c*x] Cos[c*x] - x == x*Sqrt[1 + (c*Sin[c*x])^2], {x, .25, .55}, WorkingPrecision -> 100]
%t A197021 RealDigits[t]   (* x coordinate of tangency point *)
%t A197021 y = Cos[c*t]    (* y coordinate of tangency point *)
%t A197021 radius = Cos[c*t] - t/(c*Sin[c*t])
%t A197021 RealDigits[radius]   (* A197021 *)
%t A197021 slope = -c*Sin[c*t]  (* slope at tangency point *)
%Y A197021  Cf. A197020, A196022, A196026, A197027, A197016.
%K A197021 nonn,cons
%O A197021 0,1
%A A197021 _Clark Kimberling_, Oct 08 2011