# Math Help - Exact value of sin-1(sin(7(pi/2))

1. ## Exact value of sin-1(sin(7(pi/2))

Hi, its me again. Hope I'm not asking too many math questions.
I know f( f^-1(x)) = x but is it the same for f^-1(f(x)) ?/

If it is; sin^ -1(sin(7(pi/2))) = 7pi/2 ?

Thanks !

2. if you are in doubt, check it with a calculator,

"sin^ -1(sin(7(pi/2))) = 7pi/2"

3. Originally Posted by pacman
if you are in doubt, check it with a calculator,

"sin^ -1(sin(7(pi/2))) = 7pi/2"
The range of the inverse sin function is, by definition, [-pi/2, pi/2]. Since sin(7 pi/2) = -1 it follows that $\sin^{-1} \left(\sin \left( \frac{7 \pi}{2} \right) \right) = \sin^{-1} (-1) = - \frac{\pi}{2}$.