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

%I #10 Feb 07 2025 16:44:06

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

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

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

%N Decimal expansion of greatest x satisfying 2*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="/A200127/b200127.txt">Table of n, a(n) for n = 1..10000</a>

%e least x: -0.530633047496848880166804175671064100...

%e greatest x: 1.4652353861426318569459268305726949...

%t a = 2; 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, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.54, -.53}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200126 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.46, 1.47}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200127 *)

%o (PARI) a=2; b=-3; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 01 2018

%Y Cf. A199949.

%K nonn,cons,changed

%O 1,2

%A _Clark Kimberling_, Nov 14 2011