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Thursday, February 16, 2006

Unfortunate scribe # 9

First and foremost, HAPPY BIRTHDAY VAN! Now that we got that out of the way, hi everyone this is Teddie, thanks to janet I'm your scribe for today.

hmmm, where to begin, today was a two period class day. We started off the day with waiting about 10 minutes for Mr. K and wondering if we had a spare today. Then he started off the class with telling us a story about a university course he took (linear whatchamacallit) with this one most hated prof, because of his "I don't care about you" attitude. Then some wise cracks *ahem(Calvin) *ahem(Van) went and asked him to try to teach our class at the university level. So he went and tried it, he zoomed through a bunch of information (about half a unit) and finished it in less than 10 minutes. Now everyone is stunned and I'm running out of lead.

PERIOD 2

Then we started discussing the final parameter C (a.k.a. PHASE SHIFT) in this sinusoidal function: AsinB(x-C) + D.
C is expressed in terms of pi or radians, well at least for now because that's the units our x-axis is measured in for the time being. So what C does is, if it is negative the graph shifts to the right C units, and if it is positive the graph will shift left C units. Yes this rather confusing, so lets have an example!

Consider this equation:

(x - 3 )^2 = 0
root(x-3)^2 = root0
x - 3 = 0
x = 3

The basic graph that's related to this equation is x^2. So, C = -3. So when we solved this equation, we found that
x = 3. Therefore, the graph shifts right 3 units from the origin.

PERIOD 4

We started off the afternoon with 2 questions. One was to draw a graph from looking at an equation and the other was to look at the graph and write the equation. It may look rather confusing at first, but there is one mnemonic that will really help, DABC!

D - the vertical shift
A - the amplitude
B - the time it takes the wave to complete one cycle
C - the horizontal shift

Then we did a quiz that was worth 16 marks. The quiz was without a calculator and was mainly based on memorizing the exact values for sin, cos, tan, cot, csc, sec.

Now onto the notes for today that go into our math dictionary:

SINUSOIDAL FUNCTIONS

THE GENERAL FORM

y = AsinB(x-C) + D y = AcosB(x-C) + D


THE ROLE OF PARAMETER A

A is called THE AMPLITUDE
A determines the distance, from the sinusoidal axis, of all max and min values of the function
A creates a VERTICAL STRETCH (for A > 0 ) VERTICAL COMPRESSION (for 0 < A < 1 )

THE ROLE OF PARAMETER B

B is not the PERIOD
B determines the PERIOD by this relation

PERIOD = 2pi / B also B =2pi / PERIOD

The PERIOD is "how long" (a length along the x-axis) it takes the function to "make one wave."

THE ROLE OF PARAMETER C

C is called THE PHASE SHIFT aka the HORIZONTAL SHIFT.

WARNING: WATCH THE SIGN OF C

C > 0 The graph shifts right C units
C < 0 the graph shifts left C units
note: in this equation: y = sin(x + pi / 2) C = -pi / 2

THE ROLE OF PARAMETER D

D is called the SINUSOIDAL AXIS
aka the VERTICAL SHIFT
aka the AVERAGE VALUE of the function

D > 0 the graph shifts up D units
D < 0 the graph shifts down D units

Well that's all for now, oh wait the next scribe....who to pick? drum roll plz............
the next scribe will be MARK!



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1 Comments:

At 3/01/2006 5:42 PM, Blogger Regine said...

haha. It's so colourful. The colours are hypnotizing, yet they make my head hurt. It's late, but nice scribe. It's understandable so people who have missed this class can understand it. i like the colours..

 

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