Equation of Harmonic Wave

Theorem
Let $\phi$ be a harmonic wave which is propagated along the $x$-axis in the positive direction with constant velocity $c$.

Then $\phi$ can be expressed using the equation:
 * $\forall x, t \in \R: \map \phi {x, t} = a \map \cos {x - c t}$

Proof
From Wave Profile of Harmonic Wave