A196772 Decimal expansion of the number c for which the curve y=1/x is tangent to the curve y=sin(x-c), and 0 < x < 2*Pi; c = Pi - sqrt(r) - arccos(r-1), where r=(1+sqrt(5))/2 (the golden ratio).

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

Offset: 0

Author

Clark Kimberling, Oct 06 2011

Keywords

• nonn
• cons

Examples

			c=0.965016109773342910082904125880052671050...
		

Crossrefs

Cf. A195625, A196767.

Programs

Mathematica

Plot[{Sin[x + .97], 1/x}, {x, 0, Pi}]
r = GoldenRatio; x = Sqrt[r];
c = N[Pi - x - ArcCos[r - 1], 100]
RealDigits[c]      (* A196772 *)
slope = N[-1/x^2, 100]
RealDigits[slope]  (* 1-r *)