# How do you find the x intercepts for y=sec^2x-1?

Aug 1, 2016

$\pi + \pi n = x$

#### Explanation:

Note that ${\sec}^{2} x - 1 = {\tan}^{2} x$. Hence, we can replace the original equation for a simpler one. Albeit working with $\sec$ is also easy in this case, it's a good habit to work with fewer terms. (There are occasions in which this is not true, but that will with experience.)

Also, note that the only way for ${\tan}^{2} x = 0$ is when $\tan x = 0$.
So, when is it zero? If you remember the unit circle, you can see that $\tan x = \frac{o}{a}$, where $o$ is the opposite side in the unit circle, and $a$ the adjacent.

Hence, you want $o = 0$. And that happens when $\pi + \pi n = x$, where $\pi$ is any integer.
Here's a graphical representation:
graph{tanx [-10, 10, -5, 5]}