Like, say, $z=x^2+y^2$ looks like a generalized form of $z=x^2$ (& $z=y^2$) and the later can be derived by putting $y=0$ (& $z=0$). Also, graphically the later looks like a segment/slice of the former. Similar, is the case about the equation of sphere and equation of circle. What about the case of sine (&cosine) function?
Is there any list/theory where I can find such generalized functions?