A200019 - OEIS

%I #9 Jun 24 2018 16:41:01

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

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

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

%N Decimal expansion of greatest x satisfying x^2 - 2*cos(x) = sin(x).

%C See A199949 for a guide to related sequences.  The Mathematica program includes a graph.

%H G. C. Greubel, <a href="/A200019/b200019.txt">Table of n, a(n) for n = 1..10000</a>

%e least x:  -0.8096299991295524131861096984840271321...

%e greatest x: 1.254187962477919553363912326321801374...

%t a = 1; b = -2; c = 1;

%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.9, -.8}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200018 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200019 *)

%o (PARI) a=1; b=-2; c=1; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 24 2018

%Y Cf. A199949.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 12 2011