# What does sec pi/2 equal?

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#### Explanation

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#### Explanation:

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9
Oct 16, 2015

The secant function can't be evaluated in $\frac{\pi}{2}$.

#### Explanation:

Just apply the definition and evaluate:

$\sec \left(x\right) = \frac{1}{\cos} \left(x\right)$

Thus,

$\sec \left(\frac{\pi}{2}\right) = \frac{1}{\cos} \left(\frac{\pi}{2}\right)$

But since $\cos \left(\frac{\pi}{2}\right)$ 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 $\frac{\pi}{2}$ and negative after, we will have that

${\lim}_{x \setminus \to {\left(\frac{\pi}{2}\right)}^{+}} \sec \left(x\right) = \infty$, and

${\lim}_{x \setminus \to {\left(\frac{\pi}{2}\right)}^{-}} \sec \left(x\right) = - \infty$

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