Sinusoidal function
From Calculus
Contents
Definition
As a linear transform of the sine function
The term sinusoidal function refers to a function of the form where and are linear functions and is the sine function. Specifically, it is a function of the form:
Here:
 is the mean value about which the function is oscillating, i.e., the graph of a function looks like a scaled sine function about the horizontal line .
 is the amplitude of oscillations, i.e., the function oscillates between a minimum value of and a maximum value of .
 is the angular frequency parameter and controls the period of oscillations, which is given by .
 is a phase parameter that roughly describes the head start of the function relative to a function that starts at its mean value at .
As a linear combination of sine and cosine functions
The term sinusoidal function can be used for a function of the form:
Conversion between the two versions
Here's how we convert the linear combination version to the linear transform version:
 remain the same.
 Set .
 Set as an angle so that and . is uniquely determined up to additive multiples of .
Here's how we convert the linear transform version to the linear combination version:
 remain the same.
 .
 .
Examples
Function  How it's a sinusoidal function in the linear transform sense  How it's a sinusoidal function in the linear combination sense 

sine function  : 

cosine function  
. 
sinesquared function  

cosinesquared function  
