> What do you mean? "sin(0) = 0, cos(0) = 1, and for all x, sin'(x) = cos(x), cos'(x) = -sin(x)" is perfectly unambiguous.
It's pretty straightforward. "sin(0) = 0" is not a differential equation. Any phase shift applied to sine and cosine will produce exactly the same set of differential equations that apply to sine and cosine; you can rename the shifted functions "sine" and "cosine" and you'll be fine.
It's pretty straightforward. "sin(0) = 0" is not a differential equation. Any phase shift applied to sine and cosine will produce exactly the same set of differential equations that apply to sine and cosine; you can rename the shifted functions "sine" and "cosine" and you'll be fine.