What is the domain of `(5)/(tan(x)-((1)/(sqrt(3))))`

Expert Answers
lemjay eNotes educator| Certified Educator

`f(x)= 5/(tan(x)-1/sqrt3)`

Notice that the variable x is in the denominator. So to determine the domain, we need to take note that in fractions a zero denominator is not allowed. That means that there is a restriction in our domain.

To determine the restrictions in the domain, set the denominator equal to zero and solve for x.

`tanx-1/sqrt3=0`

`tanx=1/sqrt3`

`x=tan^(-1)1/sqrt3`

`x=30^o` and `210^o`

Hence, 30 and 210 degrees are not included in our domain.

Also, take note that in tangent function, when the angle is 0, 270 and 360 degrees, it is undefined.

So, 0, 270 and 360 degrees are not included in the domain.

Therefore, the domain of the function are all real numbers except `360k` , `30+360k` , `210+360k` , and `270+360k` degrees, where k is any integer.

aruv | Student

`f(x)=5/(tan(x)-1/sqrt(3))`

The domain of function f(x) is al real numbers except where

`tan(x)-1/sqrt(3)=0`

`tan(x)=1/sqrt(3)`

`tan(x)=tan(pi/6)`

`x=npi+pi/6,` where n is an integer.

Thus domain of f(x) is

`R-{x:x=npi+pi/6 , n in Z}`

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