A197480 Decimal expansion of least x>0 having cos(2x)=(cos 4x)^2.

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

			0.5688719664527277788947249300275041747924021...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A197476.

Programs

Mathematica

b = 2; c = 4; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .55, .57}, WorkingPrecision -> 200]
RealDigits[t] (* A197480 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi/4}]
RealDigits[ ArcCos[ Root[ -2 + 4#^2 - 4#^4 + #^6 & , 2]/2], 10, 99] // First (* Jean-François Alcover, Feb 19 2013 *)