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

%I #11 Feb 12 2025 11:22:00

%S 2,7,4,1,8,5,9,2,8,0,5,9,8,3,1,5,7,9,0,1,2,9,3,8,5,7,6,1,6,5,9,2,6,1,

%T 0,6,7,1,9,3,4,6,4,4,2,6,5,9,6,6,3,7,1,8,4,8,3,7,3,1,3,2,8,7,6,3,4,5,

%U 8,4,4,1,6,6,5,1,5,9,0,3,6,8,1,0,1,8,6,6,3,2,2,3,7,2,6,9,8,8,1

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

%C See A199949 for a guide to related sequences. The Mathematica program includes a graph.

%H G. C. Greubel, <a href="/A200111/b200111.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e least x: -0.2741859280598315790129385761659261067...

%e greatest x: 1.25741142949475925602237309814803895...

%t a = 2; b = -1; c = 3;

%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -.28, -.27}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200111 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.25, 1.26}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200112 *)

%o (PARI) a=2; b=-1; c=3; solve(x=-.28, -.27, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018

%Y Cf. A199949.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Nov 13 2011