A196832 Decimal expansion of the number c for which the curve y=1/(1+x^2) is tangent to the curve y=c*sin(x), and 0 < x < 2*Pi.

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

Offset: 0

Author

Clark Kimberling, Oct 07 2011

Keywords

• nonn
• cons

Examples

			c=0.21175267284313356422891828878302637078159516791...
		

Crossrefs

Cf. A196825.

Programs

Mathematica

Plot[{1/(1 + x^2), .205 Sin[x]}, {x, 0, Pi}]
t = x /. FindRoot[x^2 + 2 x*Tan[x] + 1 == 0, {x, 2, 3}, WorkingPrecision -> 100]
RealDigits[t]     (* A196831 *)
c = N[Csc[t]/(1 + t^2), 100]
RealDigits[c]     (* A196832 *)
slope = N[c*Cos[t], 100]
RealDigits[slope] (* A196833 *)

PARI

t=solve(x=2,3, x^2 + 2*x*tan(x) + 1); 1/sin(t)/(1 + t^2) \\ Charles R Greathouse IV, Feb 22 2025