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 A197022 Decimal expansion of the radius of the circle tangent to the curve y=cos(4x) at points (x,y) and (-x,y), where 0
 3, 0, 4, 6, 7, 5, 3, 6, 3, 3, 0, 6, 6, 0, 7, 4, 5, 2, 4, 0, 2, 1, 6, 8, 4, 3, 1, 6, 6, 7, 7, 5, 8, 1, 9, 5, 4, 8, 5, 6, 3, 6, 3, 6, 9, 6, 8, 1, 4, 2, 8, 7, 7, 9, 1, 0, 1, 1, 4, 9, 8, 1, 8, 4, 3, 6, 2, 9, 3, 8, 8, 3, 2, 7, 2, 6, 0, 2, 1, 7, 2, 3, 5, 2, 6, 2, 5, 4, 5, 3, 2, 3, 4, 0, 4, 7, 2, 7, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Let (x,y) denote the point of tangency.  Then x=0.294083445311344461181635110698988639348667... y=0.384312064643508105468613486692501669417807... slope=-3.69281299167871547859350850472131295652... (The Mathematica program includes a graph.) LINKS EXAMPLE radius=0.30467536330660745240216843166775819548... MATHEMATICA r = .304; c = 4; Show[Plot[Cos[c*x], {x, -.5, .5}], ContourPlot[x^2 + (y - r)^2 == r^2, {x, -1, 1}, {y, -1, 1}], PlotRange -> All, AspectRatio -> Automatic] t = x /. FindRoot[    c*Sin[c*x] Cos[c*x] - x == x*Sqrt[1 + (c*Sin[c*x])^2], {x, .25, .55}, WorkingPrecision -> 100] RealDigits[t]  (* x coordinate of tangency point *) y = Cos[c*t]   (* y coordinate of tangency point *) radius = Cos[c*t] - t/(c*Sin[c*t]) RealDigits[radius]  (* A197022 *) slope = -c*Sin[c*t] (* slope at tangency point *) CROSSREFS Cf. A197020, A196021, A196026, A197027, A197016. Sequence in context: A188720 A113792 A216105 * A112238 A111493 A190181 Adjacent sequences:  A197019 A197020 A197021 * A197023 A197024 A197025 KEYWORD nonn,cons AUTHOR Clark Kimberling, Oct 08 2011 STATUS approved

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Last modified April 23 12:15 EDT 2021. Contains 343204 sequences. (Running on oeis4.)