Kellen Zantow Presents Sine and Cosine functions
I did these functions because I don’t think people
really know how they work and I would like to help everyone that I can.
If you have any questions feel free to contact Mr.
Young at dyoung7@prodigy.net or dyoung@fayar.net
This document will be dealing with sine and cosine functions
in the form of 
or 
such that
A = amplitude (how high or low the graph goes if A=1 then sine or cosine both go from [-1,1]
B = ratio of the new period to the normal period which is 
.
C = phase shift (initial x position)
D = initial y position.
The original Graph of Sine looks
like: 
The original Graph of Cosine looks like: 
with the
same window as before, set in Radians, not Degrees.
When given a question straight from 
like #59, examine the whole question before
solving. #59 reads: [II] Suppose the general equation 
is to be applied to a
mass in Fig. 10.24 where the cycle is to begin at t=0 with m released with zero speed at -3 m. What must 
equal?
So when doing this problem I had no clue how to start out.
So I figured out that the amplitude was 3 because it starts at -3, so that is
the max it will be able to stretch. Now
the equation looks something like this: 
. After figuring that
out I went and added what else I knew like at t=0 the distance was -3, so now
the equation looks something like this: 
then 
then 
. After that I had to figure out when the cosine function
could be equal to -1. So I went around the unit circle on the x components,
because cosine is x/r. and r is always equals 1 on the unit circle, so I had to
find when x was equal to -1, and that was -1 so our problem is solved. So in
the end, 
so the graph moved to
the right 1 unit.
This sine and cosine function could be used to graph all sorts of oscillations such as swinging pendulum, such as a wrecking ball about to plow over a house, and many others.
http://members.shaw.ca/ron.blond/sc.APPLET/index.html
http://faculty.ed.umuc.edu/~swalsh/Math%20Articles/Graphing%20Sin%20Cos.html
http://curvebank.calstatela.edu/unit/unit.htm
http://www.google.com/search?hl=en&q=Sine+and+cosine+functions
http://www.mcasco.com/trig.html
http://www.thinkwell.com/marketing/sampleNotes/PCL_note.pdf