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I noticed the following difference, and I wonder if it's a problem of my system or the results difference is actually due to the two different versions

oldsa = {0.29289321881345254` - 
    0.6666666666666666` Sin[0.5235987755982988` + phi] == 
   0.75` Cos[psi1], -0.7071067811865475` + h + 
    0.6666666666666666` Cos[0.5235987755982988` + phi] == 
   0.75` Sin[psi1], -0.5` + 
    0.6666666666666666` Sin[0.5235987755982988` - phi] == 
   0.75` Cos[psi2], -0.4660254037844386` + h + 
    0.6666666666666666` Cos[0.5235987755982988` - phi] == 
   0.75` Sin[psi2]}

NSolve[oldsa, {h, phi, psi1, psi2}]

gives solutions in Mathematica version 7, and no solution in ver. 8 Both run on Ubuntu 12.04 x64 Do you get the same resuts?

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    $\begingroup$ Yes, I find the same issue, it works in ver.7 and ver.9 yielding a list of 24 solutions and also this message : NSolve::ifun: Inverse functions are being used by NSolve, so some solutions may not be found; use Reduce for complete solution information. >> but it does not work in ver.8 i.e. it yields {}. $\endgroup$
    – Artes
    Dec 20, 2012 at 11:38
  • $\begingroup$ Haha not only that, but, in v8, if you apply the replacement rule /. 0.5235987755982988` -> π/6 it DOES produce a solution $\endgroup$
    – gpap
    Dec 20, 2012 at 11:50
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    $\begingroup$ Confirming. Solution in 7 on Linux and no solution in 8.0.4 on Windows. $\endgroup$
    – Andreas Lauschke
    Dec 20, 2012 at 11:59
  • $\begingroup$ @Artes Well, in my v8, if you define oldsa2 = oldsa/. 0.5235987755982988` -> π/6 (i.e. copy-paste the numerical value from within the trig functions and replace it with its symbolic equivalent), then NSolve[oldsa, {h, phi, psi1, psi2}] gives {} and NSolve[oldsa2, {h, phi, psi1, psi2}] gives a list of solutions of length 24! $\endgroup$
    – gpap
    Dec 20, 2012 at 12:57
  • $\begingroup$ To all the commenters, thank you guys $\endgroup$
    – Fabio Dalla Libera
    Dec 20, 2012 at 13:09

1 Answer 1

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Just adding to how strange this is in version 8 where the code below has been tested.

First, observe that the numerical value within the trigonometric function (0.523599) is $ \pi/6 $:

0.5235987755982988`== π/6

gives

True

Now, as above, define the equation to solve

oldsa = {0.29289321881345254` - 
0.6666666666666666` Sin[0.5235987755982988` + phi] == 
0.75` Cos[psi1], -0.7071067811865475` + h + 
0.6666666666666666` Cos[0.5235987755982988` + phi] == 
0.75` Sin[psi1], -0.5` + 
0.6666666666666666` Sin[0.5235987755982988` - phi] == 
0.75` Cos[psi2], -0.4660254037844386` + h + 
0.6666666666666666` Cos[0.5235987755982988` - phi] == 
0.75` Sin[psi2]}

and a version of it with the numerical value of $ \pi/6 $ replaced by the symbolic π/6, i.e.

oldsaSymbolic = oldsa/. 0.5235987755982988` -> π/6

Indeed, 

NSolve[oldsa, {h, phi, psi1, psi2}]

gives

{}

But

NSolve[oldsaSymbolic, {h, phi, psi1, psi2}]

gives 24 solutions!?!

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