A200105 - OEIS

%I #8 Jun 25 2018 22:53:54

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

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

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

%N Decimal expansion of least x satisfying x^2 - 4*cos(x) = 4*sin(x), negated.

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

%H G. C. Greubel, <a href="/A200105/b200105.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.698933604732903309337989544733567956233...

%e greatest x: 1.7695688743727017491150784620016277547...

%t a = 1; b = -4; c = 4;

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

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.7, -.6}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200105 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.76, 1.77}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200106 *)

%o (PARI) a=1; b=-4; c=4; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 25 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 13 2011