**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 : **

https://en.wikipedia.org/wiki/Sine#/media/File:Circle_cos_sin.gif

**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.

References :

http://www.allaboutcircuits.com/textbook/alternating-current/chpt-1/ac-waveforms/

https://en.wikipedia.org/wiki/Sine_wave

http://www.learningaboutelectronics.com/Articles/Why-are-sine-waves-so-used-and-important

http://www.samlexamerica.com/support/faqs/faq02.aspx

http://whatis.techtarget.com/definition/cosine-wave