Question

How do you find vertical asymptote of tangent?

Answer 1

I assume that you are asking about the tangent function, so `tan theta`. The vertical asymptotes occur at the NPV's: `theta=pi/2+n pi, n in ZZ`.

Recall that `tan` has an identity: `tan theta=y/x=(sin theta)/(cos theta)`. This means that we will have NPV's when `cos theta=0`, that is, the denominator equals 0.

`cos theta=0` when `theta=pi/2` and `theta=(3pi)/2` for the Principal Angles. Normally, we have 2 solutions, but the spacing between these 2 angles are the same, so we have a single solution,

`theta=pi/2+n pi, n in ZZ` in radians or
`theta=90+180n, n in ZZ` for degrees.

To find the vertical asymptote of ANY function, we look for when the denominator is 0.