Question

What is the asymptote of `sec(x+90°)`?

Answer 1

See ezplanation and graphical depiction.

Explanation:

`y = sec ( x +pi/2) = 1/cos ( x + pi/2 ) = -1/sin x`

The aymptotes are given by

{x = a solution of the denominator sin x = 0 }

{ x = k pi }, k = 0, +-1, +-2, +-3, ...#

See graph, for asymptotes:
graph{ (y sin x + 1 )(x+0y)(x-pi+0y)(x+pi+0y)(x-2pi+0y)(x+2pi+0y)(x-3pi+0y)(x+3pi+0y) = 0}