Question

Sin(arcsec(x))

Answer 1

So, I have already done the algebra for this problem, and I get sqrt(x^2-1)/x.
My question is, why do some books put an absolute value on the x?

Answer 2

The put the abs value bars on the x in the denominator, why?

Answer 3

*they

Answer 4

If you look at this page

http://www.intmath.com/analytic-trigonometry/7-inverse-trigo-functions.php

you'll see that the range of arcsecant is 0 < y < pi

so essentially the domain of sin(x) in this case is 0 < x < pi since arcsec(x) is the input of the sine function. This is why sine is always positive

so they're forcing x to be positive when they stick those absolute value bars around it

Answer 5

Your explanation made a lot of sense, thank you

Answer 6

you're welcome