A197690 Decimal expansion of Pi/(4 + 2*Pi).

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

Offset: 0

Author

Clark Kimberling, Oct 17 2011

Keywords

• nonn
• cons

Comments

Least x > 0 such that sin(b*x)=cos(c*x) (and also sin(c*x)=cos(b*x)), where b=2 and c=Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

Examples

			0.30550773517582864469029769397698443086...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A197682.

Programs

Mathematica

b = 2; c = Pi;
t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .3, .31}]
N[Pi/(2*b + 2*c), 110]
RealDigits[%]  (* A197690 *)
Simplify[Pi/(2*b + 2*c)]
Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]