You can use a LUT, but that's not required to define sin and cos. You can define them perfectly fine as

sin(kπ) = 0 sin(kπ + ½π) = (-1)^k cos(kπ) = (-1)^k cos(kπ + ½π) = 0 dsin/dx = -cos dcos/dx = sin

Sine and cosine are the only smooth continuous functions that are solutions to that system of equations. There are also numerous geometric ways to define them. That's what's meant by "understanding". If all you had was the LUT and no other way to compute the value of sine, then you don't really understand what sine is.