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%I #13 Jun 24 2018 08:56:42
%S 2,2,3,5,8,0,9,2,8,2,0,6,4,5,6,9,1,2,1,1,1,5,2,6,4,1,4,8,3,1,7,0,1,9,
%T 8,4,4,2,4,8,0,4,9,2,0,3,9,2,6,5,3,9,0,4,0,4,3,4,1,5,0,9,1,3,0,2,6,0,
%U 5,2,4,8,0,6,1,5,1,6,5,3,9,7,5,3,5,0,8,8,3,7,8,7,4,1,9,3,2,6,9
%N Decimal expansion of greatest x satisfying x^2 + 3*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="/A199962/b199962.txt">Table of n, a(n) for n = 1..10000</a>
%e least x: 0.7589622035176968518571982860561050925949...
%e greatest x: 2.23580928206456912111526414831701984424...
%t a = 1; b = 3; c = 4;
%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, .75, .76}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199961 *)
%t r = x /. FindRoot[f[x] == g[x], {x, 2.2, 2.3}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199962 *)
%o (PARI) a=1; b=3; c=4; solve(x=2, 3, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y Cf. A199949.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Nov 12 2011
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