Thursday, September 20, 2007

"A Scribe of Excellence"

WOW!!! Very sorry for the lateness of this scribe. I have just returned from "An Evening of Excellence" (for those who don't know: our school's awards ceremony) at which, I must add, our Calculus class did quite exceptionally. =D Now here I go with my Scribelicious post:

As we all took our seats in class today, we were presented with a picture of waves, which could only mean one thing: TRIGONOMETRY. It was in fact a review of the stuff we had learned in our previous years.
The first thing that we were told to do is take a look at the page on the Weather Network's web page, choose a statistic and find a periodic (sinusoidal) function that would fit the data. Of course we used our calculators, so this wasn't too difficult. We found that the two best fits for a sinusoidal function were MAXIMUM TEMPERATURE and SUNSHINE.
Next, we entered the real review part of the lesson; we were given a graph of a sinusoidal function and were told to write two equations for it. (see questions and answers here.)
Now there are two formulae that may be used to write an equation:
f(x)=Asin[B(x-C)]+D and f(x)=Asin(Bx-BC)+D
The first is the easier one to derive from a graph and it is the way it was originally taught to most of us. The other is there because it is possible that you might see functions written either way on an exam or test.
The parameters of these formulae are as follows (just a refresher):
A = AMPLITUDE(vertical stretch)
B = PERIOD STRETCH(determines the Period via 2π/B)
C = PERIOD SHIFT(horizontal shift)
D = SINUSOIDAL AXIS(vertical shift)
***REMEMBER: when using your calculator to find an equation(STAT, SinReg), it will appear as f(x)=Asin(Bx+C)+D. The B has not yet been factored out, and C is being added, not subtracted. Therefore, to find the value of C, divide by -B!!!***
After that quick review, we received a question that gave us an equation of a function and told us to graph them...
So, when graphing these functions, take a look at the given functions and compare them to the ones above. The next step is to figure out the value of each parameter make sure B is factored outside the brackets!!! Then just follow these easy steps:
1. Using the AMPLITUDE and SINUSOIDAL AXIS, determine the max. and min. of the graph. Then scale y-axis accordingly. Draw a dotted line for the Sinusoidal Axis.
2. Using p=2π/B, determine the period of the graph and scale the x-axis from -P to P unless otherwise instructed. Scale the axis with a mark on each quarter of the period.
3. Draw dots (outline) using the PERIOD SHIFT to determine the starting x-coordinate on the Sinusoidal Axis. The starting position depends on which trigonometric function is being used and the sign of the AMPLITUDE.
4. Finally draw a smooth, fluid curve that connects each point. NO SHARP CORNERS OR EDGES!!!.
Next Mr. K. flipped quickly to a review on the Trigonometric Identities, but did not have much time to go over it. Maybe we'll go over it in class, but just in case, take a quick look at it on SLIDE 6. He also announced that we will be having a quick MENTAL MATH quiz on the values of the Unit Circle... make sure to look over that before you go to bed tonight.

The HOMEWORK for tonight is: Exercise 1.10 Questions #1,2,3,5,6,13.


Now playing: Linkin Park - Shadow Of The Day
via FoxyTunes

1 comment:

aichelle s. said...

I enjoyed your scribe post very much...excellent use of colour and great explanations.