A197580 Decimal expansion of least x > 0 having cos(Pi*x/2) = cos(2*x)^2.

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

Offset: 0

Author

Clark Kimberling, Oct 16 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

			x=0.498636515479998285832191728772322697066045637...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = Pi/2; c = 2; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .49, 5}, WorkingPrecision -> 200]
RealDigits[t] (* A197580 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2}]