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A200122 Decimal expansion of least x satisfying 2*x^2 - 3*cos(x) = 2*sin(x), negated.

%I A200122 #11 Feb 12 2025 12:59:50
%S A200122 7,0,4,1,5,9,4,5,7,0,3,7,1,2,2,5,5,2,6,8,1,0,5,8,3,3,3,4,9,9,4,8,3,4,
%T A200122 8,2,1,0,8,4,3,1,6,2,4,3,5,8,1,8,1,8,9,5,8,7,2,3,4,8,6,8,3,2,0,2,1,0,
%U A200122 3,1,9,1,2,5,1,0,3,4,6,4,2,0,1,2,0,4,1,8,7,0,2,4,7,1,3,4,6,5,4
%N A200122 Decimal expansion of least x satisfying 2*x^2 - 3*cos(x) = 2*sin(x), negated.
%C A200122 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200122 G. C. Greubel, <a href="/A200122/b200122.txt">Table of n, a(n) for n = 0..10000</a>
%H A200122 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200122 least x: -0.70415945703712255268105833349948348210...
%e A200122 greatest x: 1.210301102156057859192844246759434780...
%t A200122 a = 2; b = -3; c = 2;
%t A200122 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200122 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A200122 r = x /. FindRoot[f[x] == g[x], {x, -.71, -.70}, WorkingPrecision -> 110]
%t A200122 RealDigits[r]  (* A200122 *)
%t A200122 r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
%t A200122 RealDigits[r]  (* A200123 *)
%o A200122 (PARI) a=2; b=-3; c=2; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 29 2018
%Y A200122 Cf. A199949.
%K A200122 nonn,cons
%O A200122 0,1
%A A200122 _Clark Kimberling_, Nov 14 2011