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A199959 Decimal expansion of least x satisfying x^2 + 3*cos(x) = 3*sin(x). 3

%I

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

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

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

%N Decimal expansion of least x satisfying x^2 + 3*cos(x) = 3*sin(x).

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

%H G. C. Greubel, <a href="/A199959/b199959.txt">Table of n, a(n) for n = 1..10000</a>

%e least x: 1.046472542540093403618073553786437093400...

%e greatest x: 1.9905034616684938355818760222044124763...

%t a = 1; b = 3; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199959 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.99, 2.0}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199960 *)

%o (PARI) a=1; b=3; c=3; solve(x=1, 1.5, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018

%Y Cf. A199949.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 12 2011

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Last modified August 20 07:48 EDT 2019. Contains 326143 sequences. (Running on oeis4.)