A332503 Decimal expansion of the number v such that the maximal normal distance between sine and cosine is the distance between (u, sin u) and (v, sin v), where u is the number u' in A332501; see Comments.

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

Offset

1,1

Comments

Let S and C denote the graphs of y = sin x and y = cos x. For each point (u, sin u) on S, let S(u) be the line normal to S at (u, sin u), and let (snc u, cos(snc u) be the point of intersection of S(u) and C. Let d(u) be the distance from (u,sin u) to (snc u, cos(snc u)). We call d(u) the u-normal distance from S to C and note that in [0,Pi], there is a unique number u' such that d(u') > d(u) for all real numbers u except those of the form u' + k*Pi. We call d(u') the maximal normal distance between sine and cosine, and we call snc the sine-normal-to-cosine function. See A332500.

Links

Table of n, a(n) for n=1..86.

Formula

v = 3Pi/4 - u, where u is given by A332501.

Example

v = 1.96870408298082320586768578622442620...

Mathematica

u = u /. FindRoot[u - 3 Pi/4 == Sin[u], {u, 1}, WorkingPrecision -> 120]  (* A332501 *)
v = 3 Pi/2 - u   (* A332503 *)
RealDigits[v][[1]]

Crossrefs

Cf. A332500, A332501, A086751.

Sequence in context: A257345 A110637 A092943 * A196501 A292819 A066766

Adjacent sequences: A332500 A332501 A332502 * A332504 A332505 A332506

Keyword

nonn,cons

Author

Clark Kimberling, May 05 2020

Status

approved