Every visualization of an electromagnetic wave is essentially some variation of this picture:
In every one of these graphs, both the electric and magnetic components are shown as being sine waves with the same phase angle. However, it is just as frequently stated that the amplitude of a magnetic field is related to the derivative of the electric field at any given point in space and/or time. Shouldn’t it follow, then, that the magnitude of any given point along the magnetic wave should peak when the corresponding point along the electric wave is at 0? In other words, if the electric component of an EM wave were a sine wave (with no phase angle), shouldn’t the magnetic component be a cosine wave (also with no phase angle)?