A200008 - OEIS

%I #13 Jun 24 2018 16:41:29

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

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

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

%N Decimal expansion of least 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="/A200008/b200008.txt">Table of n, a(n) for n = 0..10000</a>

%e least x:  0.4039548562770990578793534464221104111...

%e greatest x: 0.5924702907925039329312822762880632483...

%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=0, .5, 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