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

cos (3z + pi) = 0      using a trig identity, we have :

cos(3z)cos(pi)  - sin(pi)sin(3z)     =  0

-cos(3z)  = 0

cos(3z)  = 0

cos(z)  = 0   at   pi/2 + n*pi

So

3z  = pi/2 + n*pi       divide both sides by 3

z = pi/6  + n* (pi/3)   where n is any integer

Solve for z:
-cos(3 z) = 0

Multiply both sides by -1:
cos(3 z) = 0

Take the inverse cosine of both sides:
3 z = pi/2+pi n  for  n element Z

Divide both sides by 3:
Answer: | z = pi/6+(pi n)/3  for  n element Z