Solve for $x$ on the indicated domain.

1. $\cos x = 0$, $[0, 2π]$

   Hint (a):

   

2. $2 \sin x + \sqrt { 2 } = 0$, $[0, 2π]$

   Step (b):

   $\text{sin }x=-\frac{\sqrt{2}}{2}$

   

3. $\cos x(2 \sin x + \sqrt { 2 }) = 0$, $[0, 2π]$

   Hint (c):

   Use the Zero Product Property. Then combine parts (a) and (b).

4. $\cos x(2 \sin x + \sqrt { 2 }) = 0$

   Hint (d):

   Solve for all solutions.
   Add a $2πn$ to each solution in $[0,2π]$ where $n$ is any integer.