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

1 Answer
Apr 18, 2018

Answer:

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

Explanation:

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.