cp's OEIS Frontend

A200010 Decimal expansion of least x satisfying x^2 - cos(x) = sin(x), negated.

%I A200010 #15 Feb 12 2025 04:51:39
%S A200010 5,6,0,9,8,7,7,2,9,2,3,5,9,1,1,3,7,5,2,7,7,4,3,7,0,2,8,5,3,3,6,6,8,2,
%T A200010 3,1,7,9,9,0,9,2,1,5,5,1,9,4,7,5,5,4,2,4,5,2,8,3,2,9,7,2,2,5,4,0,7,4,
%U A200010 4,5,9,4,6,4,3,0,6,8,8,2,4,4,1,5,5,2,8,5,5,6,6,3,2,9,2,4,0,7,9
%N A200010 Decimal expansion of least x satisfying x^2 - cos(x) = sin(x), negated.
%C A200010 See A199949 for a guide to related sequences. The Mathematica program includes a graph.
%H A200010 G. C. Greubel, <a href="/A200010/b200010.txt">Table of n, a(n) for n = 0..10000</a>
%H A200010 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200010 least x:  -0.560987729235911375277437028533668231799...
%e A200010 greatest x: 1.14955462727747318906952249474440902011...
%t A200010 a = 1; b = -1; c = 1;
%t A200010 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
%t A200010 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A200010 r = x /. FindRoot[f[x] == g[x], {x, -.6, -.5}, WorkingPrecision -> 110]
%t A200010 RealDigits[r]   (* A200010 *)
%t A200010 r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
%t A200010 RealDigits[r]   (* A200011 *)
%o A200010 (PARI) a=1; b=-1; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018
%Y A200010 Cf. A199949.
%K A200010 nonn,cons
%O A200010 0,1
%A A200010 _Clark Kimberling_, Nov 12 2011