That means arccos x can only exist under certain restrictions, since an equation does not have an inverse unless its graph passes the horizontal line test. The domain of arccos x is [-1, 1] and the range is [0, pi]. Ok, so if the range can only be 0 to pi, then the graph of arccos (cos x) cannot...
Homework Statement
The problem here involves inverse trig functions. The question here is why doesn't arccos(cos x) yield the equation y = x?
Homework Equations
y = arccos(cos x)
The Attempt at a Solution
I assume the reason is due to restrictions on domain and/or range of the trig...
That's why I'm confused. It seems too simple to just change the domain in that manner and say it is a "new" domain, much less have some textbooks "disagree" with the stated domain. I'm going to e-mail my professor about this as well. Thanks for your help.
I'm confused as to why you'd restrict the domain of the sec x to -pi/2 to 3pi/2. If you used that domain as the range of the arcsec x, would that even work? The range of the arcsec x is 0 to pi. Perhaps I'm misunderstanding the question. Here it is, from the book:
In the...
If sec x = 1, then the possible values for x are pi/4 and 5pi/4.
Arcsec 1 would yield the same thing wouldn't it? Arcsec 1 is the same thing as saying what angle yields a sec of 1, which is the same thing as the sec x = 1. I know you're trying to steer me in a certain direction, but I'm not...
That was something I was somewhat confused on, whether it was asking for a new domain for the sec x or a new range arcsec x. I was looking at the domain of sec x in terms of it being a one-to-one function. So the domain previously stated creates that. I also focused on a different range for...
Homework Statement
A problem in my textbook gives the domain of sec x as [0,(pi/2)) U ((pi/2), pi]. This makes perfect sense of course. However, it is asking for an alternate domain. I've looked at the graphs of both sec x and arcsec x to try to figure out a different domain for sec x(I looked...