A plane wave like cos x lacks physical reality as it extends infinitely in the y and z directions. Despite this, it serves as a useful approximation in various scenarios due to its simplicity. Plane waves are significant because they allow for the representation of any real wave packet through Fourier decompositions. This includes both Fourier series and transforms, which facilitate analysis and understanding of complex waveforms. Overall, while idealized, plane waves play a crucial role in wave theory and applications.