 \right ]+d "This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.")
or
 \right ]+d "This is the rendered form of the equation. You can not edit this directly. Right click will give you the option to save the image, and in most browsers you can drag the image onto your desktop or another program.")
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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