Can We Trust Her?

Geometry Level 1

Michaelle asked the classroom to solve arcsinx=π\arcsin x=\pi for xx. After some minutes, she wrote the equation on the blackboard. She solved it as follows:

"Due to the fact that the arcsine of xx is defined as the inverse sine function of xx, we can write sin(arcsinx)=sinπx=sinπ\sin\left(\arcsin x\right)=\sin\pi \Rightarrow x=\sin\pi . We have that sinπ=0\sin\pi=0, so the unique solution to this equation is x=0x=0."

Is this reasoning correct?

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