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A199961 Decimal expansion of least x satisfying x^2 + 3*cos(x) = 4*sin(x).

%I A199961 #15 Feb 08 2025 23:06:14
%S A199961 7,5,8,9,6,2,2,0,3,5,1,7,6,9,6,8,5,1,8,5,7,1,9,8,2,8,6,0,5,6,1,0,5,0,
%T A199961 9,2,5,9,4,9,0,2,6,0,7,0,3,6,4,4,6,6,1,4,5,8,2,5,7,3,8,3,9,2,8,9,8,3,
%U A199961 0,8,4,2,6,2,3,5,4,9,1,4,6,4,9,2,4,6,1,2,2,8,2,3,9,2,9,2,2,4,6
%N A199961 Decimal expansion of least x satisfying x^2 + 3*cos(x) = 4*sin(x).
%C A199961 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A199961 G. C. Greubel, <a href="/A199961/b199961.txt">Table of n, a(n) for n = 0..10000</a>
%H A199961 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199961 least x:  0.7589622035176968518571982860561050925949...
%e A199961 greatest x: 2.23580928206456912111526414831701984424...
%t A199961 a = 1; b = 3; c = 4;
%t A199961 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A199961 Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
%t A199961 r = x /. FindRoot[f[x] == g[x], {x, .75, .76}, WorkingPrecision -> 110]
%t A199961 RealDigits[r]   (* A199961 *)
%t A199961 r = x /. FindRoot[f[x] == g[x], {x, 2.2, 2.3}, WorkingPrecision -> 110]
%t A199961 RealDigits[r]   (* A199962 *)
%o A199961 (PARI) a=1; b= 3; c=4; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y A199961 Cf. A199949.
%K A199961 nonn,cons
%O A199961 0,1
%A A199961 _Clark Kimberling_, Nov 12 2011