Contemplating The Wave

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

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

What else can we do to the cosine (or sine) function?

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 ...

Graph this:

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

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

Graphing Trig Functionsƒ(x) = AcosB(x - C) + Dƒ(x) = AsinB(x - C) + D

The Role of Parameter A

|A|is called the Amplitude

determines the distance of the maximum and minimum values from the Sinusoidal Axis

Acontinues ...

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:

The period is the distance along the x-axis required to make one "wave".

or

| A | > 1

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 unitsC < 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 unitsD < 0 the graph shifts down D units