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A200232 Decimal expansion of greatest x satisfying 3*x^2-2*cos(x)=2*sin(x).

%I A200232 #11 Feb 12 2025 13:04:32
%S A200232 9,6,3,2,9,1,3,7,6,6,1,9,6,7,9,1,0,4,6,5,5,6,4,1,8,2,9,6,6,4,1,6,4,2,
%T A200232 3,0,2,3,0,3,9,1,9,8,6,7,2,7,0,6,2,5,1,0,1,2,1,4,5,6,4,6,1,4,8,6,2,1,
%U A200232 1,4,2,3,8,3,8,8,9,9,3,5,1,0,0,4,1,0,9,7,1,9,4,2,1,6,6,1,4,4,8
%N A200232 Decimal expansion of greatest x satisfying 3*x^2-2*cos(x)=2*sin(x).
%C A200232 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200232 G. C. Greubel, <a href="/A200232/b200232.txt">Table of n, a(n) for n = 0..10000</a>
%H A200232 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200232 least x: -0.508066683701868134653059484203509821...
%e A200232 greatest x: 0.9632913766196791046556418296641642...
%t A200232 a = 3; b = -2; c = 2;
%t A200232 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200232 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200232 r = x /. FindRoot[f[x] == g[x], {x, -.51, -.50}, WorkingPrecision -> 110]
%t A200232 RealDigits[r]   (* A200231 *)
%t A200232 r = x /. FindRoot[f[x] == g[x], {x, .96, .97}, WorkingPrecision -> 110]
%t A200232 RealDigits[r]   (* A200232 *)
%o A200232 (PARI) a=3; b=-2; c=2; solve(x=.96, .97, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A200232 Cf. A199949.
%K A200232 nonn,cons
%O A200232 0,1
%A A200232 _Clark Kimberling_, Nov 14 2011