How do I know when $\displaystyle arcsin(sin(x))$ is
$\displaystyle x$
$\displaystyle \pi - x$ or
$\displaystyle 2\pi - x$ ?
Yea but when it's like
$\displaystyle arcsin(sin(3))$
$\displaystyle arcsin(sin(4))$
$\displaystyle arcsin(sin(5))$
I think the first one is $\displaystyle \pi-3$, second one is $\displaystyle \pi-4$ but last one is $\displaystyle \2pi-5$ (I'm going by memory from the lecture but you get what I'm saying like when it is outside that |pi/2| bound, it gets weird but I'm going to get tested on that
I don't understand why it is those values...
Let $\displaystyle y=\sin^{-1} (\sin x)$. It means if you got at a certain point on the x-axis say $\displaystyle x=\frac{\pi}{2}$ then the y-value is the output you get if you subsitute $\displaystyle x$ for $\displaystyle \frac{\pi}{2}$ in $\displaystyle \sin^{-1}(\sin \frac{\pi}{2} )$. The reason why I graphed it is so that you can just find all the values by just looking without calculating anything.