# Solving system of trigonometric equations

I have a 6x6 matrix full of sin and cos in 7 variables. I should calculate the value of the variables that makes the determinant of the matrix being 0. I have tried with the following syntax but it takes too long (no results after 2 days):

    Reduce[{Det[Jnt[φ1, φ2, φ3, φ4, φ5, φ6, φ7]] == 0 && -Pi/2 < φ1 < Pi/2 && -Pi/2 < φ2 < Pi/2 &&  -Pi/2 < \φ3 < Pi/2 && -Pi/2 < φ4 < Pi/2  && -Pi/2 < φ5 < Pi/2 && -Pi/2 < φ6 < Pi/2 && -Pi/2 < φ7 < Pi/2 }, {φ1, φ2, φ3, φ4, φ5, φ6, φ7}]


I have tried putting some fixed values for 3 variables, and then Mathematica told me that "reduce cannot solve this system..."

Any suggestion?

Thanks a lot, Luca

• Hi Luca93, welcome to mathematica.stackexchange! You can help others to help you by always presenting a minimal example including the Mathematica code along with example data, so that they may reproduce your problem on their own machines. – Henrik Schumacher Jul 15 '17 at 18:21
• thanks for your answer! is possible to attach a file? – Luca93 Jul 15 '17 at 19:19
• Because the matrix is really really long and it would be annoying to copy it in the question – Luca93 Jul 15 '17 at 19:25
• Would a numerical approach suffice? Could try minimizing either the determinant squared or perhaps the smallest singular value, as a function of the angle parameters. FindMinimum might be up to the task. – Daniel Lichtblau Jul 15 '17 at 20:44