A197268 Decimal expansion of least x>0 having sin(4x)=(sin 3x)^2.

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

Offset: 0

Author

Clark Kimberling, Oct 12 2011

Keywords

• nonn
• cons

Comments

The Mathematica program includes a graph. See A197133 for a guide to least x>0 satisfying sin(b*x)=(sin(c*x))^2 for selected b and c.

Examples

			0.4599755354050940320651507516304768327270591...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A197133.

Programs

Mathematica

b = 4; c = 3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .4, .5}, WorkingPrecision -> 100]
RealDigits[t] (* A197268 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]