can someone explain to me how arcsec infinity is equal to pi/2? thanks

Strictly speaking, "\(\displaystyle arcsec(\infty)\)"

**isn't** \(\displaystyle \pi/2\) or any other number. "\(\displaystyle \infty\)" isn't a number so secant is not defined for it. You could, of course, extend the real number system to include "infinities" but there are several different ways to do that- you would have to specify which you meant.

But, we can talk about this in the

**limit** sense. \(\displaystyle sec(\theta)= \frac{1}{cos(\theta)}\) and as \(\displaystyle \theta\) goes to \(\displaystyle \pi/2\), \(\displaystyle cos(\theta)\) goes to 0 and so \(\displaystyle sec(\theta)= \frac{1}{cos(\theta)\) "goes to infinity" (get larger without bound). Thus, if we extend the real numbers sytem in that way, we have that "\(\displaystyle sec(\pi/2)= \infty\)" and so "\(\displaystyle arcsec(\infty)= \pi/2\)".