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1st Hour PreCal
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The image above is of a cosine function. |
The Cosine |
The Cosine function is a very strange trigonometric=
function. It shows how a per=
iod can be shown, such as a pendulum swinging back and forth, with a functi=
on. The general function for =
the cosine function is: y =
=3D Acos(B(x-C))+D A =3D amplitude (from middle of height to peak) B =3D 2pi/p =
Where P =3D the x value from 1 max to the next C =3D H.Shift =
; (Time when the first peak occurs) D =3D V.Shift (how much above x axis amplitude is)<= o:p> |
=
An Example... |
Created by: Michael McClendon because this is one o=
f the few trigonometric functions that is understood him. Contact Michael at icezstorms@gmail.com. |
Now make a plot with DAYH as x and DAYT as y. |
In order to get A, subtract the maximum from the mi=
nimum. In this case the max i=
s 365 and the min is 141; you must then divide this number by 2; thus, the =
A is 224. Now to get the B go from the first max the secon=
d max and subtract the x’s. =
span>So, the B is 2pi/11. Now=
for the C… This is the=
easiest part of the cosine, just trace to the first maximum and record the=
x. (2). To get the D, you mu=
st get the A and then subtract the maximum from it. Now, let’s piece it all together… and ba=
m you get 112cos(2pi/11(x-2))+253 which should look like this. |
You are probably asking yourself, ‘why would =
I need to know this’? W=
ell if you ever want to join the Army and want to figure out how far you ca=
n shoot your missile, while dealing with a repeating pattern of wind gusts&=
#8230; this would give the best time (A).&=
nbsp; Or, if you want to design a pendulum driven clock, this would =
show the pattern of the pendulum as it should be, so you would know whether=
or not you messed up. =
Yay? |