A259258 Decimal expansion of the smallest positive solution to sin(x) + cos(x) + tan(x) = 0.

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

Offset

1,1

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 = 1 in the first approximation. See A259259 for the other solution set.

Links

Table of n, a(n) for n=1..110.

Example

4.0905606739537756911944516590724078...

Mathematica

RealDigits[2*Pi - ArcCos[y/.Solve[y*(y^3+y^2-1)==1/2]][[3]], 10, 120][[1]] (* Vaclav Kotesovec, Jul 07 2015 *)
RealDigits[x/.FindRoot[Sin[x]+Cos[x]+Tan[x]==0, {x, 4}, WorkingPrecision-> 120]][[1]] (* Harvey P. Dale, Sep 23 2020 *)

Prog

(PARI) default(realprecision, 2000); s=solve(x=3, 4.3, tan(x)+cos(x)+sin(x)); for(n=1, 100, print1(floor(s)%10, ", "); s=10*s)

Crossrefs

Cf. A259259.

Sequence in context: A187172 A296570 A241667 * A291716 A022899 A364101

Adjacent sequences: A259255 A259256 A259257 * A259259 A259260 A259261

Keyword

nonn,cons

Author

Derek Orr, Jun 22 2015

Status

approved