A197134 Decimal expansion of least x>0 having sin(x)=(sin 3x)^2.

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

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

			0.115402267387127882859236747957368...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A197133.

Programs

Mathematica

b = 1; c = 3; f[x_] := Sin[x]
t = x /.  FindRoot[f[b*x] == f[c*x]^2, {x, .1, .3}, WorkingPrecision -> 100]
RealDigits[t] (* A197134 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]
RealDigits[ ArcCos[ Root[ 17 - 112 #^2 + 352 #^4 - 512 #^6 + 256 #^8 &, 4]], 10, 100] // First (* Jean-François Alcover, Feb 19 2013 *)

PARI

acos(polrootsreal(256*x^8-512*x^6+352*x^4-112*x^2+17)[4]) \\ Charles R Greathouse IV, Feb 12 2025

Extensions

Digits from a(79) on corrected by Jean-François Alcover, Feb 19 2013