Find all solutions to the equation cos(3z+π)=0.

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Hello!

As you probably know, there are many solutions of the equation `cos(w)=0.`

 

The general solution is  `w=+-pi/2+2 k pi,`

where `k` is any integer. Without `+-` it may be written as two sequences,

`w_1=pi/2+2k pi` and `w_2=-pi/2+2k pi.`

 

In our problem `w=3z+pi,` so

`3z+pi=pi/2+2k pi` or `3z+pi=-pi/2+2k pi.`

 

These equations are linear for `z` and may be solved easily:

`z_1=-pi/6+(2k pi)/3` and `z_2=-pi/2+(2k pi)/3.`

This is the answer (remember that `k` is any integer).

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