A197485 Decimal expansion of least x>0 having cos(4x)=(cos(6x))^2.

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

Offset: 0

Author

Clark Kimberling, Oct 15 2011

Keywords

• nonn
• cons

Comments

The Mathematica program includes a graph. See A197476 for a guide for the least x>0 satisfying cos(b*x)=(cos(c*x))^2 for selected b and c.

Examples

			0.34054490912143700309252640816391426246259292812...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A197476.

Programs

Mathematica

b = 4; c = 6; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .34, .35}, WorkingPrecision -> 100]
RealDigits[t] (* A197485 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1/2}]
RealDigits[ ArcTan[ Sqrt[ Root[7#^4 - 68#^3 + 106#^2 - 68# + 7&, 1] ] ], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)