# Thread: question on arcsec infinity

1. ## question on arcsec infinity

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

2. Originally Posted by FailCalculus
can someone explain to me how arcsec infinity is equal to pi/2? thanks
$\displaystyle \sec \theta=\frac{1}{\cos \theta}$

Set the denominator to be 0

3. Originally Posted by FailCalculus
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 "$\displaystyle arcsec(\infty)= \pi/2$".

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