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

1 Answer
Aug 1, 2016

pi+pin=x

Explanation:

Note that sec^2x-1=tan^2x. 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^2x=0 is when tanx=0.
So, when is it zero? If you remember the unit circle, you can see that tanx=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+pin=x, where pi is any integer.
Here's a graphical representation:
graph{tanx [-10, 10, -5, 5]}