Friday February 26th Class

Today in class we started off by taking the quiz.
After the quiz we went over some questions on the homework. We did problems 27 and 55.
27.


To graph these two functions we first looked at a standard sin graph.
http://fooplot.com/index.php
Then we took the f(x) function and altered the graph by moving the Y values of 1 to -2, and the Y values of -1 to 2. (Red)
We added on to that axis the g(x) function onto the same graph. This transformed the original sin graph by changing all the Y values of 1 to 4 and Y values of -1 to -4. (Blue)
file:///Users/student/Desktop/sin.tiff
The period is still 2π, and the symmetry is odd, as it is for all sin graphs. This means sin(-x)=-sin(x)
The transformation of these two functions changed the amplitude of the sin function.

55.
We then changed this to to make it simpler to graph.
This graph looked like: file:///Users/student/Desktop/cos.tiff
The period was 4π and the amplitude was changed, along with the graph being condensed. This graph originally (before being transformed) had was even, being symmetrical across the Y axis as all cos graphs originally are.

After reviewing the homework we moved on and looked at the graphs of the trig functions. We noticed that the sin graph and cos graph were very similar, but just shifted over to the right a bit. Both had a domain of -1 to 1 and a range of all real numbers.
We spent most of the rest of class playing with these graphs. We also looked at the graphs of the other trig functions as well and looking at the periods and amplitudes of the graphs.
We also looked at the tan graph which looks like:file:///Users/student/Desktop/tan%20graph.tiff

The csc graph which looks like:file:///Users/student/Desktop/csc%20graph.tiff

And the sec graph which looks like:file:///Users/student/Desktop/sec%20graph.tiff

But we did not get into why they are the way they are. That will be learned later and is in Dan's scribe post of class on 3/2.