Question

Explain the range and domain of tan x function????
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Answer 1

Answer:

Domain of tan x function :-

tan x function is defined as ::

$f(x) = \tan \: x = \dfrac{ \sin \: x}{ \cos \: x }$

Here $\cos\:x \not = 0$. If $\cos\:x = 0$, then the $\tan\:x$ function will become undefined which is not possible.

We know that $cos\:x$ function is 0 on $x = \dfrac{ \pi}{2}$ , $\dfrac{3\pi}{2}$ , $\dfrac{5\pi}{2}\dots$

i.e. odd multiples of $\dfrac{ \pi}{2}$.

Since $\cos\:x$ function is 0 on odd multiples of π/2, odd multiples of $\dfrac{\pi}{2}$ are not allowed in $\tan\: x$ function.

So the domain of $\tan\:x$ function will be:-

${{ \sf{Domain}} = \mathbb{R} - \Big \{(2n + 1) \dfrac{ \pi}{2}}$ , ${ \: n \in \: \mathbb{Z} \Big \}}$

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Range of tan x function :-

$\tan \: x = \sf\dfrac{perpendicular}{base}$

Since the ratio of perpendicular and base can attain any value and tan x function can even be negative, range of tan x function will be -∞ to ∞.

$\sf Range = ( - \infty$ , $\infty )$