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

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, 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, 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

Offset: 0

Author

Clark Kimberling, Nov 12 2011

Keywords

• nonn
• cons

Comments

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

Examples

			least x:  -0.560987729235911375277437028533668231799...
greatest x: 1.14955462727747318906952249474440902011...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for transcendental numbers.

Crossrefs

Cf. A199949.

Programs

Mathematica

a = 1; b = -1; c = 1;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.6, -.5}, WorkingPrecision -> 110]
RealDigits[r]   (* A200010 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.2}, WorkingPrecision -> 110]
RealDigits[r]   (* A200011 *)

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