Friday, June 26, 2015

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

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...

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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