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

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nickolean | Student, College Freshman | eNotes Newbie

Posted September 27, 2010 at 9:11 AM via web

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

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neela | High School Teacher | Valedictorian

Posted September 27, 2010 at 11:54 AM (Answer #1)

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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).

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted September 27, 2010 at 11:00 AM (Answer #2)

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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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