A329933 Decimal expansion of greatest negative number x such that csc x + sec x = 1.

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

Offset

1,3

Links

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

Formula

Exact value: x = - arcsec(1/2 (1 + sqrt(-1 + 2 sqrt(2))) + sqrt(2 (-1 + 2 sqrt(2)))))

Example

least positive x:  2.6534458515135517347998055805879...
greatest negative x: -1.0826495247186551155684838889...
2.65344... - (-1.08264...) = Pi/2.

Mathematica

Solve[1/Sin[x] + 1/Cos[x] == 1, x]
Plot[1/Sin[x] + 1/Cos[x] - 1, {x, -Pi, Pi}]

Crossrefs

Cf. A329932.

Sequence in context: A178969 A019660 A021125 * A234015 A322129 A019635

Adjacent sequences: A329930 A329931 A329932 * A329934 A329935 A329936

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jan 02 2020

Status

approved