What SI unit is defined as one full wavelength that takes one second to cycle through 360° of phase?

The correct choice is Hertz, which is the unit of frequency in the International System of Units (SI). Hertz is defined as one cycle per second. Therefore, when you refer to a full wavelength that completes one cycle in one second, this precisely aligns with the definition of Hertz. Specifically, in the context of waves, if a wave completes one full oscillation or wavelength every second, it has a frequency of one Hertz. This concept is fundamental in various fields of physics and engineering, particularly in wave mechanics, sound waves, and electromagnetic waves.

In summary, Hertz quantifies the frequency of cycles per second, making it the correct unit for the scenario described in the question regarding the full wavelength with a cycle period of one second.