What does sec pi/2 equal?

The secant function can’t be evaluated in ##pi/2##.

Just apply the definition and evaluate:

##sec(x)=1/cos(x)##

Thus,

##sec(pi/2)=1/cos(pi/2)##

But since ##cos(pi/2)## is zero, this division is not legit.

We can calculate the limit, so see if it’s positive or negative infinite. Since the cosine function is positive before ##pi/2## and negative after, we will have that

##lim_{xto (pi/2)^+} sec(x)=infty##, and

##lim_{xto (pi/2)^- } sec(x)=-infty##