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A200011 Decimal expansion of greatest x satisfying x^2 - cos(x) = sin(x). 3

%I

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

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

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

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

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

%H G. C. Greubel, <a href="/A200011/b200011.txt">Table of n, a(n) for n = 1..10000</a>

%e least x: -0.560987729235911375277437028533668231799...

%e greatest x: 1.14955462727747318906952249474440902011...

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

%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, -.6, -.5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200010 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200011 *)

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

%Y Cf. A199949.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 12 2011

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Last modified October 20 20:04 EDT 2019. Contains 328270 sequences. (Running on oeis4.)