What is the formula for sine waves?

Hint:The sine wave is described as the waveform in which the amplitudes are always proportional to the displacement angle at every point. The sine or sinusoidal wave is a curve that describes the smooth repetitive oscillation.

Complete step by step solution:
A Sinusoidal wave is a form of the geometrical wave which oscillates up, down, right and left. It is used to reduce the complexity of the wave that is coming in the mathematical formulation. The basic formulation of the sine wave is written as;
\[y(t) = A\sin (2\pi ft + \varphi )\]
And it is also written it as;
\[y(t) = A\sin (\omega t + \varphi )\]
here, $\omega = 2\pi ft$
The sine wave is shown in the figure below,

Image: Sinusoidal wave

In the mathematical expression we have the following representation which is defined as;
1. $A$ is defined as the amplitude of the sine wave. It is defined as the maximum displacement or distance covered by the sinusoidal wave when the body is vibrating.
2. $f$ is defined as the frequency. It is defined as the number of repeating events that can occur at a particular time.
3. $t$ is known as the time period of vibration.
4. $\varphi $ is known as a phase. It is defined as the relationship between the two sine waves.
5. $\omega $ is known as the angular frequency.

Hence formula of sine wave is \[y(t) = A\sin (\omega t + \varphi )\].

Note: There are three characteristics that separate the two or more sinusoid waves from each other. These characteristics are known as amplitude. Frequency and the phase. The application of the sine wave is that it is used in the transmission because it is a more efficient form of a wave as compared to the other waves.