cp's OEIS Frontend

A200011 Decimal expansion of greatest x satisfying x^2 - cos(x) = sin(x).

%I A200011 #14 Feb 12 2025 04:51:42
%S A200011 1,1,4,9,5,5,4,6,2,7,2,7,7,4,7,3,1,8,9,0,6,9,5,2,2,4,9,4,7,4,4,4,0,9,
%T A200011 0,2,0,1,1,3,9,6,8,1,7,7,9,1,3,9,2,4,4,8,1,3,1,9,2,5,2,4,8,6,3,4,8,5,
%U A200011 5,1,5,3,5,9,0,5,7,3,7,8,3,9,3,2,6,2,5,3,2,9,9,1,6,6,5,1,2,9,2
%N A200011 Decimal expansion of greatest x satisfying x^2 - cos(x) = sin(x).
%C A200011 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200011 G. C. Greubel, <a href="/A200011/b200011.txt">Table of n, a(n) for n = 1..10000</a>
%H A200011 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200011 least x:  -0.560987729235911375277437028533668231799...
%e A200011 greatest x: 1.14955462727747318906952249474440902011...
%t A200011 a = 1; b = -1; c = 1;
%t A200011 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200011 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A200011 r = x /. FindRoot[f[x] == g[x], {x, -.6, -.5}, WorkingPrecision -> 110]
%t A200011 RealDigits[r]   (* A200010 *)
%t A200011 r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
%t A200011 RealDigits[r]   (* A200011 *)
%o A200011 (PARI) a=1; b=-1; c=1; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y A200011 Cf. A199949.
%K A200011 nonn,cons
%O A200011 1,3
%A A200011 _Clark Kimberling_, Nov 12 2011