The general form of the **cosine ** function can be written as

#y = A * cos( Bx+-C) +-D#, where

#|A|# - amplitude;

#B# - cycles from #0# to #2pi# -> #period = (2pi)/B#;

#C# - horizontal shift (known as phase shift when #B# = 1);

#D# - vertical shift (displacement);

#A# affects the graph's amplitude, or half the distance betwen the maximum and minimum values of the function. this means that increasing #A# will vertically stretch the graph, while decreasing #A# will vertically shrink the graph.

#B# affects the function's period. SInce the cosine's period is #(2pi)/B#, a value of #0 < B<1# will cause the period to be greater than #2pi#, which will stretch the graph horizontally.

If #B# is greater than #1#. the period will be less than #2pi#, so the graph will shrink horizontally. A good example of these is

http://www.regentsprep.org/regents/math/algtrig/att7/sinusoidal.htm

Vertical and horizontal shifts, #D# and #C#, are pretty straightforward, these values only affecting the graph's vertical and horizontal positions, not its shape.

Here's a good example of vertical and horizontal shifts:

http://www.sparknotes.com/math/trigonometry/graphs/section3.rhtml