A196758 Decimal expansion of the number c for which the curve y=1/x is tangent to the curve y=c*sin(x), and 0 < x < 2*Pi.

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

Offset: 0

Author

Clark Kimberling, Oct 06 2011

Keywords

• nonn
• cons

Examples

			c=0.5495393993551534115219389873253839380900...
		

Crossrefs

Cf. A196624.

Programs

Mathematica

Plot[{1/x, .55*Sin[x]}, {x, 0, Pi}]
xt = x /. FindRoot[x + Tan[x] == 0, {x, 1.5, 2.5}, WorkingPrecision -> 100]
RealDigits[xt] (* A196504 *)
c = N[1/(xt*Sin[xt]), 100]
RealDigits[c]  (* A196758 *)
slope = -1/xt^2
RealDigits[slope]  (* A196759 *)

PARI

t=solve(x=2,3, sin(x)-x/sqrt(1+x^2)); 1/t/sin(t) \\ Charles R Greathouse IV, Feb 11 2025