Pre-Cal 40S Slides February 19, 2008
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Transcript of Pre-Cal 40S Slides February 19, 2008
![Page 2: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/2.jpg)
Sketch each of the following graphs without using a calculator ...
![Page 3: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/3.jpg)
![Page 4: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/4.jpg)
Now, put what you've learned together, graph this function ...
![Page 5: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/5.jpg)
What else can we do to the cosine (or sine) function?
fooplot an online graphing calculator
![Page 6: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/6.jpg)
![Page 7: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/7.jpg)
![Page 8: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/8.jpg)
![Page 9: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/9.jpg)
![Page 10: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/10.jpg)
Sketch each of the following graphs without using a calculator ...
![Page 11: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/11.jpg)
Sketch each of the following graphs without using a calculator ...
![Page 12: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/12.jpg)
![Page 13: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/13.jpg)
Sketch each of the following graphs without using a calculator ...
![Page 14: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/14.jpg)
Graph this:
![Page 15: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/15.jpg)
Now, put what you've learned together, graph this function ...
![Page 16: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/16.jpg)
Sketch each of the following graphs without using a calculator ...
![Page 17: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/17.jpg)
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 ...
![Page 18: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/18.jpg)
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
![Page 19: Pre-Cal 40S Slides February 19, 2008](https://reader036.fdocuments.us/reader036/viewer/2022081404/559288c11a28ab43468b47a0/html5/thumbnails/19.jpg)
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