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A200006 Decimal expansion of least x satisfying 3*x^2 + cos(x) = 4*sin(x).

%I A200006 #15 Feb 12 2025 04:50:15
%S A200006 3,1,9,1,6,5,5,8,4,4,9,3,9,5,6,1,1,4,5,0,9,4,4,8,2,8,0,4,6,1,2,3,8,7,
%T A200006 8,6,4,5,0,7,4,1,1,2,3,8,1,1,0,4,6,5,8,9,6,6,4,5,3,7,3,6,2,4,0,6,0,0,
%U A200006 9,7,9,2,3,1,2,2,5,3,6,7,3,1,2,1,1,7,2,2,3,0,9,5,8,1,8,9,0,8,2
%N A200006 Decimal expansion of least x satisfying 3*x^2 + cos(x) = 4*sin(x).
%C A200006 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200006 G. C. Greubel, <a href="/A200006/b200006.txt">Table of n, a(n) for n = 0..10000</a>
%H A200006 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200006 least x:  0.31916558449395611450944828046123878...
%e A200006 greatest x: 0.9357819545602016906476903567483506551...
%t A200006 a = 3; b = 1; c = 4;
%t A200006 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200006 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A200006 r = x /. FindRoot[f[x] == g[x], {x, .31, .32}, WorkingPrecision -> 110]
%t A200006 RealDigits[r]  (* A200006 *)
%t A200006 r = x /. FindRoot[f[x] == g[x], {x, .93, .94}, WorkingPrecision -> 110]
%t A200006 RealDigits[r]  (* A200007 *)
%o A200006 (PARI) a=3; b=1; c=4; solve(x=0, .5, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y A200006 Cf. A199949.
%K A200006 nonn,cons
%O A200006 0,1
%A A200006 _Clark Kimberling_, Nov 12 2011