what is the domain of the function y=tan x

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thilina-g | College Teacher | (Level 1) Educator

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The domain of a function f(x) are the x values in which the function f(x) is defined.

Now before we go on to find the domain of tan(x), we shall use our trignometric knowledge to see where tan(x) is defined and not defined.

Actually tan(x) is not defined at pi/2, and it is defined at pi. And if you go further tan(x) is not defined at (3pi/2) also. Again it is defined at 2pi. Agian it is not defined at 5pi/2. At all those values tan(x) goes to infinity.

So we make an important observation that, tan(x) is not defined at the odd multiples of pi/2, negative or positive, such as, -3(pi/2),-1(pi/2), (pi/2),3(pi/2),5(pi/2) and so on.

So the domain of tan should be any real number excluding the odd multiples of  (pi/2).

So in mathematics terms we can write this as,

`D(tan(x) = {x|x!= npi + pi/2 , ninZZ:x inRR}`

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