ABSTRACT
Compound angles are required, for example, in the analysis of acoustics, where a beat is interference between two sounds of slightly different frequencies, and with phase detectors which is a frequency mixer, analogue multiplier, or logic circuit that generates a voltage signal which represents the difference in phase between two signal inputs. Many rational functions of sine and cosine are difficult to integrate without compound angle formulae. Two periodic functions of the same frequency may be combined by plotting the functions graphically and combining ordinates at intervals or resolution of phasors by drawing or calculation. In general, when the current through an inductance is increasing, energy is transferred from the circuit to the magnetic field, but this energy is returned when the current is decreasing.
