What does sec pi/2 equal?

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What does sec pi/2 equal?

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Answer 1 · 2015-10-16T10:50:59

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

Explanation:

Just apply the definition and evaluate:

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

Thus,

$sec (\frac{π}{2}) = \frac{1}{cos (\frac{π}{2})}$ $sec(pi/2)=1/cos(pi/2)$

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

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

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

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What does sec pi/2 equal?

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