How do you find the asymptotes for $f( x ) = tan(x)$ ?

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Answer 1 · 2018-04-18T18:49:44

$tanx$ has vertical asymptotes at $x=(pi/2)+npi$

Determine the values of $x$ for which $tanx$ doesn't exist.

Recall that $tanx=sinx/cosx.$ If $cosx=0, tanx$ does not exist due to division by zero.

We know $cosx=0$ for $x=(pi/2)+npi$ where $n$ is any integer.

Therefore, $tanx$ has vertical asymptotes at $x=(pi/2)+npi$ .

No horizontal asymptotes exist for the tangent function, as it increases and decreases without bound between the vertical asymptotes.

How do you find the asymptotes for f( x ) = tan(x)f( x ) = tan(x)?