A259259 Decimal expansion of the largest negative solution to sin(x) + cos(x) + tan(x) = 0 (negated).

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

Offset

0,1

Comments

There are two unique real solutions to this equation, up to a multiple of 2*Pi. One is x ~ 2*Pi*n - 2.18722 and the other is x ~ 2*Pi*n - 0.443144. This decimal expansion is for n = 0 in the second approximation. See A259258 for the other solution set.

Links

Table of n, a(n) for n=0..107.

Example

-0.443143645780469743105815193852418815...

Mathematica

RealDigits[ArcCos[y/.Solve[y*(y^3+y^2-1)==1/2]][[4]], 10, 120][[1]] (* Vaclav Kotesovec, Jul 07 2015 *)

Prog

(PARI) default(realprecision, 2000); s=abs(solve(x=-1, 0, tan(x)+cos(x)+sin(x))); for(n=1, 100, s*=10; print1(floor(s)%10, ", "))

Crossrefs

Cf. A259258.

Sequence in context: A010657 A019706 A016497 * A369882 A194668 A378793

Adjacent sequences: A259256 A259257 A259258 * A259260 A259261 A259262

Keyword

nonn,cons

Author

Derek Orr, Jun 22 2015

Status

approved