Question

What is the domain and range of arcsec(x), and WHY? I know the domain and range, but I don't understand why.

Answer 1

arcsecant tells you the angle given a ratio, so the input has to be a ratio that is defined for 1/cos(x) and the range is the possible angles that have that ratio.

Answer 2

the domain of arcsecant is the range of secant. if you know what the range of secant is, then that explains the domain of arcsecant.

Answer 3

the range however is arbitrarily chosen, since secant is a periodic function, there are an infinite number of values of \(x\) for which say \(\sec(x)=2\)
in order to make the function well defined, you need to pick a range so that the function is not multivalued. i.e. you have to decide by convention which particular \(x\) you will pick that satisfies the equation \(\sec(x)=2\)

Answer 4

Thanks for both of your responses. They both really helped me understand how to deal with arcsec(x) :D

Satellite73, your second post was really helpful, thanks!