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

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f(x) = ln(cosx)

Here f(x) is real when the logarithm is of positive values.

Therefore cosx > 0 for ln(cosx) to exist.

cosx > 0 when x is in ithe interval : 90 degree <=x =< 90 degree or pi/2 radian <=x=< pi/2 radian . This could be expressed in the interval notation as: x in the interval (-90 deg , 90 deg) or x is in the interval (-pi/2 radian , pi/2 radian).

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)**

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