A196767 - OEIS

%I #11 Aug 09 2021 14:07:32

%S 2,0,7,3,9,3,2,8,0,9,0,9,1,2,1,4,9,0,1,1,6,7,7,7,6,2,9,7,7,9,9,3,6,0,

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

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

%N Decimal expansion of the least x > 0 satisfying 1 = x*sin(x - Pi/2), or, equivalently, -1 = x*cos(x).

%e x=2.073932809091214901167776297799360067946219531...

%t Plot[{1/x, Sin[x], Sin[x - Pi/2], Sin[x - Pi/3], Sin[x - Pi/4]}, {x,

%t   0, 2 Pi}]

%t t = x /. FindRoot[1/x == Sin[x], {x, 1, 1.2}, WorkingPrecision -> 100]

%t RealDigits[t]  (* A133866 *)

%t t = x /. FindRoot[1/x == Sin[x - Pi/2], {x, 1, 2}, WorkingPrecision -> 100]

%t RealDigits[t]     (* A196767 *)

%t t = x /. FindRoot[1/x == Sin[x - Pi/3], {x, 1, 2}, WorkingPrecision -> 100]

%t RealDigits[t]   (* A196768 *)

%t t = x /. FindRoot[1/x == Sin[x - Pi/4], {x, 1, 2}, WorkingPrecision -> 100]

%t RealDigits[t]    (* A196769 *)

%t t = x /. FindRoot[1/x == Sin[x - Pi/5], {x, 1, 2}, WorkingPrecision -> 100]

%t RealDigits[t]   (* A196770 *)

%t t = x /. FindRoot[1/x == Sin[x - Pi/6], {x, 1, 2}, WorkingPrecision -> 100]

%t RealDigits[t]    (* A196771 *)

%Y Cf. A196772.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 06 2011