A199951 Decimal expansion of least x satisfying x^2 + cos(x) = 3*sin(x).

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

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:  0.36356053985895926625732148372284398566895...
greatest x: 1.771792952982026337265923586449094216220...
		

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 = 3;
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, .36, .37}, WorkingPrecision -> 110]
RealDigits[r]  (* A199951 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.77, 1.78}, WorkingPrecision -> 110]
RealDigits[r]  (* A199952 *)

PARI

a=1; b=1; c=3; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018