freeCodeCamp/guide/english/mathematics/amplitude-and-period-of-sinusoidal-functions-from-equation/index.md

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title: Amplitude and Period of Sinusoidal Functions from Equation
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## Amplitude and Period of Sinusoidal Functions from Equation

The **generic equation** for a sinusoidal function is:

![Generic Sinusoid Equation](https://github.com/viso-gio/HostedImages/blob/master/GenericSinusoid.png?raw=true)

Where *A* represents the **amplitude** of the oscillation, and *f* the **frequency**.
*Phi* is the **phase**, linked to the amount by which the sinusoid is shifted along the *x* axis.
*Omega* is the **angular frequency**, and represents the rate of oscillation as radians per second.

The **period** of the oscillation, *T*, is given by:

![Period](https://github.com/viso-gio/HostedImages/blob/master/PeriodFormula.png?raw=true)



A commonly found **alternative form** of the sinusoid is:

![Alternative Sinusoid Equation](https://github.com/viso-gio/HostedImages/blob/master/AlternativeSinusoid.png?raw=true)

In this case, the **amplitude** is calculated as:

![Alternative Amplitude](https://github.com/viso-gio/HostedImages/blob/master/AlternativeAmplitude.png?raw=true)

#### More Information:

For more informations visit:
* <a href='https://www.mathsisfun.com/algebra/amplitude-period-frequency-phase-shift.html' target='_blank' rel='nofollow'>MathIsFun</a>
* <a href='https://en.wikipedia.org/wiki/Sine_wave' target='_blank' rel='nofollow'>Wikipedia: Sine Wave</a>