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A200231 Decimal expansion of least x satisfying 3*x^2-2*cos(x)=2*sin(x).

%I A200231 #11 Feb 12 2025 13:04:22
%S A200231 5,0,8,0,6,6,6,8,3,7,0,1,8,6,8,1,3,4,6,5,3,0,5,9,4,8,4,2,0,3,5,0,9,8,
%T A200231 2,1,8,9,4,8,2,6,2,6,7,3,3,4,2,3,8,3,3,0,9,1,6,6,9,1,7,6,3,5,0,8,2,6,
%U A200231 5,1,1,8,0,2,3,3,0,6,1,7,3,4,6,3,9,0,2,2,0,8,5,4,5,9,6,4,8,7,0
%N A200231 Decimal expansion of least x satisfying 3*x^2-2*cos(x)=2*sin(x).
%C A200231 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200231 G. C. Greubel, <a href="/A200231/b200231.txt">Table of n, a(n) for n = 0..10000</a>
%H A200231 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200231 least x: -0.508066683701868134653059484203509821...
%e A200231 greatest x: 0.9632913766196791046556418296641642...
%t A200231 a = 3; b = -2; c = 2;
%t A200231 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200231 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A200231 r = x /. FindRoot[f[x] == g[x], {x, -.51, -.50}, WorkingPrecision -> 110]
%t A200231 RealDigits[r]   (* A200231 *)
%t A200231 r = x /. FindRoot[f[x] == g[x], {x, .96, .97}, WorkingPrecision -> 110]
%t A200231 RealDigits[r]   (* A200232 *)
%o A200231 (PARI) a=3; b=-2; c=2; solve(x=-.51, -.50, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018
%Y A200231 Cf. A199949.
%K A200231 nonn,cons
%O A200231 0,1
%A A200231 _Clark Kimberling_, Nov 14 2011