Explain why arcsin(sin(3π/4)) ≠ 3π/4 when y = sin(x) and y = arcsin(x) are inverses.

Short and are *not* inverses. At least not perfect ones.

is a multi-valued function, i.e. not one-to-one, so it's not invertible.

On the other hand, you can restrict the domain of to a subset of the standard domain (all real numbers) over which is not multi-valued. The standard choice for this is to consider . If you have a calculator with the function built into it, this is the definition it uses. Notice that is outside this restricted domain.

This is why

Add up all the sides