And many years later...in another place, another teacher......proved entirely to my satisfaction...t
...that the y-value of each of those two curves was exactly equal to the slope of the other at any point on that x-axis.
To put it in more formal, mathematical terms; the sine function is the derivative of the cosine...and vice-versa. And once again, this has nothing to do with us, or even of the physical universe, it is all simply a property of triangles.