How many roots exist for $y=sec(x)$

Question

In the interval $( - \pi ,\ \pi ]$.There are 2 roots exist mentioned in the book. Could anyone please explain how?

Exact question from book : Let $Y=\sec X$ .Compute $f_Y(y)$ in terms of $f_X(x)$ .What is $f_Y(y)$ when $f_X(x)$ is uniform in $[ −π,π )$ ?

Answer 1

Hint #1: Draw the graph (or use a graphing program) of $\sec (x) \ \text {(or} \ \dfrac {1}{\cos (x)})$.

Hint #2: Viewing the graph, where is $\sec (x)$ undefined?

Answer 2

$$\sec x = \frac{1}{\cos x}$$

Obviously it is impossible for $\sec x$ to become $0$ because $\frac{1}{\cos x}$ can never reach $0$. In fact, since the range of $\cos x$ is $y \in [-1, 1]$, the range of $\sec x$ becomes $y \in (-\infty, -1] \cup [1, +\infty)$. Hence, there are no real roots.