Sinusoidal waves are smooth periodic oscillations that can be represented by a sine curve. They occur often in mathematics, physics, engineering and other fields. A sine wave is defined by its amplitude, frequency, phase and can be represented by the equation Y(t)=Asine(ωt+φ). Sine waves are important because they retain their shape when added to other sine waves and are the only periodic waveform with this property, making them unique for applications like Fourier analysis. Joseph Fourier discovered sine waves can be used as building blocks to describe and approximate any periodic waveform. Sine waves have various uses including measuring earthquake intensity, generating test signals, in sensitive medical equipment, and audio/video electronics.

1. Sinusoidal waves
A sine wave or sinusoid is a mathematical curve that describes a
smooth periodic oscillation. A sine wave is a continuous wave. It
is named after the function sine, of which it is the graph. It
occurs often in pure and applied mathematics, as well as physics,
engineering, signal processing and many other fields.
: a waveform that represents periodic oscillations in which the
amplitude of displacement at each point is proportional to the sine
of the phase angle of the displacement and that is visualized as a sine
curve : SINE CURVE
Where a human driver would try to pick a line and stay on it
throughout a corner, the self-steering Audi twitches its wheel with
high-frequency corrections, scribbling a sine wave of small inputs.

2. Y(t)=Asine(ωt+φ)
• A, amplitude, the peak deviation of the function from zero.
• f, ordinary frequency, the number of oscillations (cycles) that occur
each second of time.
• ω = 2πf, angular frequency, the rate of change of the function
argument in units of radians per second
• {displaystyle varphi }, phase, specifies (in radians) where in its cycle
the oscillation is at t = 0.
• When {displaystyle varphi } is non-zero, the entire waveform
appears to be shifted in time by the amount {displaystyle varphi
}/ω seconds. A negative value represents a delay, and a positive value
represents an advance.
The sine wave is important in physics because it retains its wave shape when added to
another sine wave of the same frequency and arbitrary phase and magnitude. It is the only
periodic waveform that has this property. This property leads to its importance in Fourier
analysis and makes it acoustically unique.

3. In 1822, French mathematician Joseph Fourier discovered that sinusoidal waves can be
used as simple building blocks to describe and approximate any periodic waveform,
including square waves. Fourier used it as an analytical tool in the study of waves and
heat flow

4. Use of sinusoidal wave
1. Measuring intensity of earth quack
Measuring of generating signal in oscilloscope
Sensitive medical equipments
Audio video electronic devices (light dimmer_) etc.
Sine waves are use to technical analysis and trading help identify patterns