OFFSET
1,1
COMMENTS
Let (x,y) denote the point of tangency, where x>0:
x=2.3973091169572703557415944811143634671454653692...
y=0.7355734556385944841653303915319993812641279844...
slope=0.6774449729386857532010706302057868510403567...
(The Mathematica program includes a graph.)
EXAMPLE
radius=4.27432451693585827192680241796164720368009482...
MATHEMATICA
r = 4.27; c = 1;
Show[Plot[-Cos[c*x], {x, -5, 5}],
ContourPlot[x^2 + (y - r)^2 == r^2, {x, -5, 5}, {y, -1.5, 8.7}], PlotRange -> All, AspectRatio -> Automatic]
u[x_] := -Cos[c*x] + x/(c*Sin[c*x]);
t = x /. FindRoot[Sqrt[u[x]^2 - x^2] == u[x] + Cos[c*x], {x, 2, 3}, WorkingPrecision -> 100]
RealDigits[t] (* x coordinate of tangency point *)
y = -Cos[c*t] (* y coordinate of tangency point *)
radius = u[t]
RealDigits[radius] (* A197026 *)
slope = c*Sin[c*t] (* slope at tangency point *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 09 2011
STATUS
approved