waves - What is the theoretical/intutive meaning of $x(t) = x_0 cos ( omega t + f )$?

What is the meaning of $x(t)=x_0 \cos(\omega t+f)$, where $x_0$ is the amplitude, $\omega$ the angular frequency, $t$ time and $f$ the phase constant?

I know how to solve the mathematical problems which use this expression, but what I don't understand is how sine and cosine functions are used to express AC waves. I know the math but I do not understand the theory behind it. I do not have an intuitive understanding of these expressions. If you cannot explain at least guide me to a resource that can.

i want to understand the math in a theoretical manner like are we going to take the sine/cosine of the wt or the solved value of it, since sine/cos is a ratio so basically are we multiplying the since/cos fraction value to the variables, oh i am so confused please explain .