or
The constant factor of a in y=asinx acts as a scaling factor- a vertical stretch or vertical shrink of the basic sine curve. If 
, the basic sine curve is stretched, and if 
, the basic sine curve is shrunk. The result is that the graph of y=asinx ranges between -a and a instead of -1 and 1.
The amplitude of 
and 
represents half the distance between the maximum and minimum values of the function and is given by: 
Let b be a positive real number. The period of 
and 
is given by: 
Note that if 
, the period of is greater than 
and represents a horizontal stretching of the graph of 
. Similarly, if 
, the period of is less than and represents a horizontal shrinking of the graph of .
The constant c creates horizontal translations (shifts) of the basic sine and cosine curves.
The graph of is shifted by an amount of 
. The number is the phase shift.
The left and right endpoints of a one-cycle interval can be determined by solving the equations 
and 
.
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