The cosine function ... why does it look like this?
fooplot an online graphing calculator

Sketch each of the following graphs without using a calculator ...

Sketch each of the following graphs without using a calculator ...

Sketch each of the following graphs without using a calculator ...

Now, put what you've learned together,
graph this function ...

Graphing Trig Functions
ƒ(x) = AcosB(x - C) + D
ƒ(x) = AsinB(x - C) + D
The Role of Parameter A
|A|is called the Amplitude
A determines the distance of the maximum and
minimum values from the Sinusoidal Axis
continues ...

| A | > 1 The graph is stretched A units.
0 <| A | < 1 the graph is compressed by factor A.
A < 0 the graph is reflected over the sinusoidal axis.
The role of Parameter B.
B is not the period. B determines the period
according to this relation:
or
The period is the distance along the x-axis
required to make one \"wave\".

The role of parameter C.
C is called the phase shift. (aka the horizontal shift)
C > 0 the graph is shifted to the right C units
C < 0 the graph is shifted left C units
WARNING: watch the sign of C
The role of parameter D.
D is called the vertical shift, aka average value.
D determines the sinusoidal axis.
D > 0 the graph shifts up D units
D < 0 the graph shifts down D units