# Numerical solve question

Bug introduced in 9.0 or earlier and fixed in 10.4.0

Why does this work?

Solve[5 Tan[t] + 9 == 0 && 0 <= t < 2 Pi , t]

{{t -> π - ArcTan[9/5]}, {t -> 2 π - ArcTan[9/5]}}

But this doesn't.

NSolve[5 Tan[t] + 9 == 0 && 0 <= t < 2 Pi , t]

{}
• It does work if I do this: NSolve[5 Tan[t]+9==0&&0<=t<2 Pi,t,Complexes]. So you have to allow complex values to get the real solutions. I think that's strange.
– Jens
Oct 15, 2015 at 5:22
• NSolve[5 Tan[t] + 9 == 0 && 0 <= t <= 6, t] also works :) Oct 15, 2015 at 5:27
• NSolve[5 Tan@t + 9 == 0 && 0 <= t <= 2 Pi] Also works ! :=) Oct 15, 2015 at 5:30
• The question is out of scope for this site. The answer to this question requires either advice from Wolfram support or the services of a professional magician :) Oct 15, 2015 at 6:14
• Fixed in the development version today. Oct 20, 2015 at 16:20

It does appear that NSolve is not behaving properly, and I have forwarded an incident report to our developers with the information you provided. I would like to include a link to the stack exchange article; do you have the stack exchange article number?

I have sent a reply giving the URL of this question as requested.

Also, on the basis of this reply from WRI, I am marking the question with .

### Update

I received another email from WRI tech support concerning this issue saying the developers have agreed to fix it.

Thank you for the link to the article. I have heard back from our development team and a fix for this issue is expected in a future release.

This bug has been fixed in Mathematica 10.4.0.

NSolve[5 Tan[t] + 9 == 0 && 0 <= t < 2 Pi, t]

(* {{t -> 2.07789}, {t -> 5.21949}} *)