The correct statements regarding the secant function are as follows:
- The graph has a vertical asymptote at [tex]x = \frac{\pi}{2}[/tex].
- The graph has a vertical asymptote at [tex]x = 3\frac{\pi}{2}[/tex].
- The graph will go through point [tex]\left(\frac{\pi}{4}, \sqrt{2}\right)[/tex]
- The graph will go through point [tex]\left(\frac{\pi}{3}, 2\right)[/tex]
What is the secant function?
It is one divided by the cosine, that is:
[tex]\sec{x} = \frac{1}{\cos{x}}[/tex]
The vertical asymptotes are when the cosine is 0, that is, [tex]x = k\frac{\pi}{2}, k = 1, 2, ...[/tex]
As for the values of the function:
[tex]\sec{\left(\frac{\pi}{4}\right)} = \frac{1}{\cos{\left(\frac{\pi}{4}\right)}} = \sqrt{2}[/tex]
[tex]\sec{\left(\frac{\pi}{3}\right)} = \frac{1}{\cos{\left(\frac{\pi}{3}\right)}} = 2[/tex]
You can learn more about the secant function at https://brainly.com/question/14961055
