A197292 Decimal expansion of least x>0 having sin(6x)=(sin 3x)^2.

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

Offset

0,1

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.

Links

Table of n, a(n) for n=0..99.

Index entries for transcendental numbers.

Example

0.3690495725980301676723551533928456800...

Mathematica

b = 6; c = 3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .3, .4}, WorkingPrecision -> 100]
RealDigits[t] (* A197292 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/2}]
RealDigits[ ArcCos[ Sqrt[ Root[-1 + 45# - 120#^2 + 80#^3 & , 3]]], 10, 100] // First (* Jean-François Alcover, Feb 19 2013 *)

Crossrefs

Cf. A197133.

Sequence in context: A114157 A021275 A281802 * A232817 A346640 A247398

Adjacent sequences: A197289 A197290 A197291 * A197293 A197294 A197295

Keyword

nonn,cons

Author

Clark Kimberling, Oct 13 2011

Status

approved