Pre-Cal 40S Slides February 19, 2008

Contemplating The Wave

http://flickr.com/photos/mshandro/2188532588/

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

http://fooplot.com/

Graph this:

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

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

Pre-Cal 40S Slides February 19, 2008

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Transcript of Pre-Cal 40S Slides February 19, 2008