# Inverse Trig Functions Domain Restrictions

I read from my textbook that since trig functions (sin and cos) don't pass the horizontal line test, so to be able to consider its inverse function, we have to restrict the domain of the original domain, and consider the small piece as its inverse function.

So for arcsine, my textbook tells me to consider the interval between -90 <= x <= 90 (I know it's supposed to be pi, but it's my first time asking question here, I haven't learned how to use that format). But can I consider other interval like 0 to 180?

• "we have to restrict the domain of the original domain, and consider the small piece as its inverse function". Technically, that's not correct. What the inverse of the small piece does is indicate a unique point on the unit circle. Using that point and the properties of $\sin$, $\cos$ or whatever, you can find all other points on the unit circle that are also inverses. Commented Apr 18, 2021 at 2:50

no because you can't invert sin function between $0$ and $\pi$
infact to invert you need that the piece of function you select is bijective but $sin(x)=sin(\pi-x)$