Why are Sine Waves So Used and Important?

Sine waves are so important and so studied because the sine wave is the most basic and the most common waveform for AC Signal variations.

A rotary generator is a very important device that allows us to have electricity in our homes. Most electricity is made by turbine blades rotating at speeds high enough to produce electricity in a generator. The waveform produced by this generator is a sine wave, whose output is proportional to the angle of rotation. So this means the electricity coming out of the power sockets in our houses are sine waves. Sine waves are also produced naturally in oscillator circuits, which are circuits that have an inductor and a capacitor. If you place a capacitor and inductor in a circuit in the correct orientation, the circuit will produce a sine wave in proportion to the amount of inductance and capacitance in the circuit. Thus, sine waves are produced naturally in many circuits and devices and very important, so that's why they are so studied.