Question

How can I know that the inverses of trig functions are actually not functions at all?

Answer 1

We know that the definition of a function is that there is one y value for each x.

Explanation:

Graphically, a function inverse reflects across the line y = x. Take something like the Sine function, and imagine drawing it up the y axis instead of horizontally along x. You will end up with infinite y values for a single x value `-1 <= x <= 1`.

So, unless we apply restrictions to trig function inverses, those inverses are not functions.