How do i find the domain of the function f(x) = ln(cos(x))?

f(x) = ln(cos(x)

The domain
is  when cos(x) is a positive value.

 (cos(x)) >
0

We know that:

cos0 =
1

cos pi/2 = 0

cos pi =
-1

cos 3pi/2 = 0

cos 2pi=
1

Then cos(x) values are between -1, and
1

in order for the function to be defined, then the domain
is when cos(x) > 0  which are the interval:

(0,
pi/2) ( 3pi/2, 2pi)

Then the domain is
:

x = (0, pi/2) U (3pi/2,
2pi)