A199961 Decimal expansion of least x satisfying x^2 + 3*cos(x) = 4*sin(x).

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

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:  0.7589622035176968518571982860561050925949...
greatest x: 2.23580928206456912111526414831701984424...
		

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 = 3; c = 4;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .75, .76}, WorkingPrecision -> 110]
RealDigits[r]   (* A199961 *)
r = x /. FindRoot[f[x] == g[x], {x, 2.2, 2.3}, WorkingPrecision -> 110]
RealDigits[r]   (* A199962 *)

PARI

a=1; b= 3; c=4; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018