1st Hour PreCal

The image above is of a cosine function.

The Cosine

The Cosine function is a very strange trigonometric function.  It shows how a period can be shown, such as a pendulum swinging back and forth, with a function.  The general function for the cosine function is:

y = Acos(B(x-C))+D

A = amplitude (from middle of height to peak)

B = 2pi/p  Where P = the x value from 1 max to the next

C = H.Shift  (Time when the first peak occurs)

D = V.Shift (how much above x axis amplitude is)

First need to download DAYH and DAYT

An Example...

DAY’s Cosine Page

DAY’s Home Page

Mathworld

AnalyzeMath

CosEngine

Test Yourself

GraphHelp

Created by: Michael McClendon because this is one of the few trigonometric functions that is understood him.  Contact Michael at [email-masked].

Now make a plot with DAYH as x and DAYT as y.

In order to get A, subtract the maximum from the minimum.  In this case the max is 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 second max and subtract the x’s.  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 must get the A and then subtract the maximum from it.  Now, let’s piece it all together… and bam 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’?  Well if you ever want to join the Army and want to figure out how far you can shoot your missile, while dealing with a repeating pattern of wind gusts… this would give the best time (A).  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?