A200009 - OEIS

%I #13 Jun 24 2018 18:36:14

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

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

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

%N Decimal expansion of greatest x satisfying 4*x^2 + cos(x) = 4*sin(x).

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

%H G. C. Greubel, <a href="/A200009/b200009.txt">Table of n, a(n) for n = 0..10000</a>

%e least x:  0.4039548562770990578793534464221104111...

%e greatest x: 0.59247029079250393293128227628806324...

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

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

%t Plot[{f[x], g[x]}, {x, .3, .7}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .40, .41}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200008 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .59, .60}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200009 *)

%o (PARI) a=4; b=1; c=4; solve(x=.5, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 12 2011