A197381 Decimal expansion of least x > 0 having sin(Pi*x/4) = sin(Pi*x/3)^2.

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

Offset: 0

Author

Clark Kimberling, Oct 14 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

			x=0.88736048447785163686131425680836901251306...
		

Crossrefs

Cf. A197133.

Programs

Mathematica

b = Pi/4; c = Pi/3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 0.8, 1}, WorkingPrecision -> 200]
RealDigits[t] (* A197381 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 2}]
(* or *)
RealDigits[12*ArcTan[Sqrt[Root[9 - 217*#1 + 1085*#1^2 - 1501*#1^3 + 1019*#1^4 - 267*#1^5 - #1^6 + #1^7 & , 2]]]/Pi, 10, 120][[1]] (* Vaclav Kotesovec, Nov 14 2015 *)