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
