Question

What is the domain of y = sec(x)?

Answer 1

$\bf sec(\theta)=\cfrac{1}{cos(\theta)}$

now, whenever the cosine function, becomes 0, it turns the rational secant function to "undefined".  that occurs at   $\bf \frac{\pi }{2},\frac{3\pi }{2}$ on the range from [0, 2π]

now, if you keep going around, it will happen at   $\bf \frac{\pi }{2}+\pi n\qquad n\in \mathbb{Z}$, or so long "n" is an integer

so... the domain for secant then, has to be anything BUT those values.

$\bf \{\theta |\qquad \theta =\mathbb{R};\qquad \theta \ne \frac{\pi }{2}+\pi n\qquad n\in \mathbb{Z}\}$

Answer 2

I chose D and it was wrong, i think it's B)all real numbers except npi+pi/2 where n is any integer