Find all solutions to the equation cos(3z+π)=0.
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).
The steps in finding the general solution:
1. Firstly you need to find your reference angle, `alpha`
`alpha=cos^-1(0) = Pi/2`
2. The format for the general solution of the cos trig ratio:
The set of all solutions to `cos(x) = y`
`x =± alpha +2kPi` or `x= -alpha +2kPi` , where k is an integer.
3. Applying the format to our solution