What does sec pi/2 equal?

1 Answer
Oct 16, 2015

Answer:

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

Explanation:

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_{x\to (pi/2)^+} sec(x)=infty#, and

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