Graphing Sine and Cosine


The absolute value of a is the amplitude of the function y=a sinx
The range of the function y=a sinx is :

The amplitude of y= a sinx and y= a cosx represents half the distance between the maximum and minimum values of the function

The period of y= a sinbx and y = a cosbx is given by:                    

One period is the same as one cycle

Example: Sketch the graph of:

The amplitude is 1, because b=1/2.
The period is
=

=  4π

The graph will reach its first peak at π and intersect the x=axis at 2π. The period will be at 4π once the graph has made one full cycle.

Cosine parent graph

Sine parent graph