A200119 - OEIS

%I #12 Feb 12 2025 11:31:33

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

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

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

%N Decimal expansion of greatest x satisfying 2*x^2 - 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="/A200119/b200119.txt">Table of n, a(n) for n = 1..10000</a>

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

%e least x: -0.46682360757098679958413415443158404...

%e greatest x: 1.3071909920738130664046341866545604...

%t a = 2; b = -2; 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, -.47, -.48}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200118 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.3, 1.31}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200119 *)

%o (PARI) a=2; b=-2; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 29 2018

%Y Cf. A199949.

%K nonn,cons,changed

%O 1,2

%A _Clark Kimberling_, Nov 14 2011