[Eldandan]

That's part of what makes it such a rich subject. Even something as simple as writing y=sin(x) has so much more embedded into it than the "input x output y" notion of functions. Parametrization of the Unit Circle, right triangles, special angles, you name it. Diving into the rabbit hole enough to convince yourself the step is justified is part of the learning process, if you're engaging with it properly. You do need to be judicious sometimes with what you decide is important to dive further into. That comes with the context/goals and experience of the reader.