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A200021 Decimal expansion of greatest x satisfying x^2 - 2*cos(x) = 2*sin(x). 3

%I

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

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

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

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

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

%H G. C. Greubel, <a href="/A200021/b200021.txt">Table of n, a(n) for n = 1..10000</a>

%e least x: -0.64004919114257711573983526967584120...

%e greatest x: 1.4763687483809203916716968897898364...

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

%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, -.65, -.64}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200020 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.47, 1.48}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200021 *)

%o (PARI) a=1; b=-2; c=2; 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

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Last modified June 22 09:57 EDT 2021. Contains 345375 sequences. (Running on oeis4.)