Final answer:
The output of the phase detector is empirically related to the signal amplitude multiplied by the cosine of the phase difference. In physics, particularly when dealing with wave interference and AC circuits, the cosine function is instrumental in determining the combined amplitude and phase relationship between the voltage and current.
Step-by-step explanation:
The output of the phase detector in a phase-angle voltmeter, which measures the difference in phase angle between two sinusoidal signals, is proportional to the signal amplitude and a trigonometric function of the phase difference between the signals. Given the options of sine, cosine, tangent, and cotangent, the phase detector's output is typically related to the cosine of the phase difference.
When considering the relationship of two interfered waves, such as in Young's double slit experiment or AC voltage application in circuits involving capacitors, the cosine function is also fundamental. For instance, the resultant amplitude of two waves traveling in the same direction with a phase difference of 180° and each with an amplitude 'A' would be zero since they are perfectly out of phase and cancel each other out. The formula A² = A₁² + A₂² + 2A1A2 cosδ represents the interference pattern of waves where δ is the phase difference.
In the context of a capacitor, an AC voltage results in the voltage following the current by a quarter of a cycle, or a 90° phase angle, which is an example of the phase shift impacting the relationship between current and voltage in an AC circuit.