A197261 Decimal expansion of least x>0 having sin(3x) = sin(2x)^2.

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

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

			0.650240618217618192095555172734670514...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A197133.

Programs

Mathematica

b = 3; c = 2; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .5, .7}, WorkingPrecision -> 100]
RealDigits[t] (* A197261 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]

PARI

asin((1+4*cos((Pi+acos(37/64))/3))/3) \\ Gleb Koloskov, Sep 15 2021

Formula

Equals arcsin((1+4*cos((Pi+arccos(37/64))/3))/3). - Gleb Koloskov, Sep 15 2021