Sine, in mathematics, is a trigonometric function of an angle.
Sine theta = Opposite side / Hypotenus.
The sine wave or sinusoid is a mathematical curve that describes a smooth repetitive oscillation. It is named after the function sine.
Any oscillation, such as a sound wave or alternating current, whose waveform is that of a sine curve.
Sine wave Relation to a circle :
Importance of Sine Wave :
- 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
Pure Sine wave :
The output voltage of a sine-wave inverter has a sine wave-form like the sine wave-form of the mains / utility voltage. In a sine wave, the voltage rises and falls smoothly with a smoothly changing phase angle and also changes its polarity instantly when it crosses 0 Volts.
In a modified sine wave, the voltage rises and falls abruptly, the phase angle also changes abruptly and it sits at 0 Volts for some time before changing its polarity.
Below fig shows pure and modified sine waves:
Sine Vs Cosine waves :
A cosine wave is a signal waveform with a shape identical to that of a sine wave , except each point on the cosine wave occurs exactly 1/4 cycle earlier than the corresponding point on the sine wave.