# Question #c8edf

Nov 17, 2017

1

#### Explanation:

By itself, $\sec \left(x\right)$ is not easy to work with, since we haven't really spent a lot of time learning the values associated with it. How can we put it in the form of something simpler? Well, remember that:

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

Hence, we'll have:

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

You should know that $\cos \left(\pi\right) = - 1$ from the unit circle. Because we're squaring the $\cos \left(x\right)$, the negative sign simply goes away, so we're left with:

$\frac{1}{1} = \textcolor{red}{1}$

Check out the graph of ${\sec}^{2} \left(x\right)$ below. Notice how it has the coordinate $\left(\pi , 1\right)$:

graph{y = (sec(x))^2 [-10, 10, -5, 5]}

Hope that helped :)