Electromagnetic waves are represented by sinusoidal curves, specifically reflecting the changing magnitudes of the electric and magnetic fields. The discussion highlights that these fields can oscillate between zero and their maximum values, illustrating their dynamic nature. This behavior is analogous to the components of a rotating vector in a plane, which also change sinusoidally with constant angular speed. The conversation seeks to clarify the underlying principles of how these magnitudes fluctuate. Understanding these concepts is crucial for grasping the behavior of classical electromagnetic waves.