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Decimal expansion of greatest x satisfying 4*x^2 - cos(x) = 4*sin(x).
3

%I #8 Jul 08 2018 21:28:37

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

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

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

%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="/A200292/b200292.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.2044255015377807131364929398797955...

%e greatest x: 0.98577638170390045503079405387981...

%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, -1, 1}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.21, -.20}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200291 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .98, .99}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200292 *)

%o (PARI) a=4; b=-1; c=4; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 08 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 15 2011