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What is the vertical asymptote of y = tan(x) ?

Answer 1

#f(x)=tan x# has infinitely many vertical asymptotes of the form: #x=(2n+1)/2pi#, where n is any integer.

We can write #tan x={sin x}/{cos x}#, so there is a vertical asymptote whenever its denominator #cos x# is zero. Since #0=cos(pi/2)=cos(pi/2 pm pi)=cos(pi/2 pm 2pi)=cdots#, we have vertical asymptotes of the form #x=pi/2+npi={2n+1}/2pi#, where #n# is any integer.

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Answer 2

Elijah Abram

The vertical asymptotes of y = tan(x) occur at x = (n + 1/2)π, where n is an integer.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.