Can We Trust Her?
Michaelle asked the classroom to solve \(\arcsin x=\pi\) for \(x\). After some minutes, she wrote the equation on the blackboard. She solved it as follows:
"Due to the fact that the arcsine of \(x\) is defined as the inverse sine function of \(x\), we can write \(\sin\left(\arcsin x\right)=\sin\pi \Rightarrow x=\sin\pi \). We have that \(\sin\pi=0\), so the unique solution to this equation is \(x=0\)."
Is this reasoning correct?