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Tuesday, May 23, 2006 

* unit's almost done.


Well, I have just looked over everything that I have to include into this scribe post for today and well....theres alot! So bare with me, sorry if its late, if i missed anything, or did anything wrong, cause i'm still learning myself. First off, we started the week off with 2 classes.

In the first class we went over a equation that we worked on last week.


So the equation was
y=-3sin4(sinx-π/8)-2
On the graph here I have shown the
y=sinx.

So when drawing out this equation you'd want to first look at
D and A of our equation. D and A of our y=AsinB(x-C)+D formula. Thats shown in red, above.

From our equation we see that
D is -2, and D is our sinusoidal axis, that is were it shows if the graph shifts either up or down x units. -2 means, that our graph shifts down 2 units. ( as shown above).

Now we look at our
A, which is our amplitude , it shows us how far away the max. and the min. are from the sinusoidal axis. From our equation our A is -3. With the negative (-) sign in front of the 3, this means that our graph starts from the minimum. So you go down 3 units. That shows the distance from the minimum to the axis.

The next thing we look at is
B, and in our equation this is 4 . So, now we need to look for the period, to do this we taken the formula 2π/B.
period=2π/B
=2π/4
=π/2 <- makes one wave.

So now, that we've got D, A, and B down, C is left. C is just where we have to shift our graph left or right on the sinusoidal axis. It shows that our C is -π/8. So we take our graph and shift it right π/8 units.

So thats, that. After that he had assigned us two problems to do at the spot. One, we were given the equation and we had to graph that. Then the second problem, we had a graph, which we had to find the functions, A, B, C, and D. And also, write the equation out for that graph. I'm not going to bother putting them up on here, because theres so much more I have to do, but if anyone does want to see the two equations, just leave a comment or something to let me know, and i'll make sure to post them up.

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2ND CLASS

So if anyone missed class this afternoon, we wrote some more in our dictionaries. Here it is.

Applications of Periodic - an example

A ferris wheel has a radius of 25 meters. It;s center is 26 meters above the ground. it rotates once every 50 seconds. SUppose you get on at the bottom at t=0.

a) graph your height above the ground during the first 2 minutes of the ride.
b) write an equation for the graph, showing heigh as a function of time.
c) find how high above the ground you are at:
i) 10 seconds ii) 20 seconds iiii) 60 seconds
d) find two times when you are 50 meters above the ground.

THE SOLUTION:
A) Draw a picture of the situation and then sketch the graph. It is also helpful to figure out the value of each parameter A, B, C, D.



1 m. above ground (min. height)

diameter is 50 m.

max. height is 51 m.






y = A sin B(x-C)+D
A=51-26=25 (radius)
B= 2π/50 [2π/period]
C=12.5 [starting point moved right 12.5, see graph]
D= 26
y=25sin[2π/50(x-12.5)]+2


The he just told us, if we wanted to find out for 2 minutes. We would just continue on with our graph, with the pattern. Yeah gets?!

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Then after our dictionaries, we got into groups and started to do an activity.

Pebble Round and Round
As tiy stio tiyr car at a traffic light, a pebble becomes wedged between the tire treads. As you start to drive, the pebble remains stuck in the tire tread, and the distance of the pebble from the pavement varies sinusoidally with the distance you drive. The period is, of course, the circumference of the wheel, and tghe wheel has a diameter of 24 inches.

(a) Sketch a graph of this function.





















(b) Write the sinusoidal equation of this function.

y=12sin(2π/75.398)(x-12.50)+26

How we got this.
Circumference = 2πr
=75.398 or 24π
D= 12
A=12
B=2π/period
=2π/75.398
C=18.8495 or 6π

(c) Caculate the distance the pebble is from the pavement after you have driven 15 inches; 100 inches; 200 inches.

So you enter the equation y=12sin((2π/75.398)(x-18.8495))+12 into [y=] in your calculator.
Then you would now have to go to your homescreen so [2nd][MODE]. From there hit the [VARS] -> Y-VARS [Functions][1: Y1]

Once Y1 is on your homescreen, put in brackets (15)
Y1(15) = -9.30
Then, with (100)
Y1(100)=-1.04
Then, (200)
but it has to be (200)(12), dont know why?! Got lost there!

EEK! Kay, I don't know if im doing this last part right, Mr. K was in such a rush I couldnt really get it, something like that? Not sure. Sorry!

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So, that was pretty much our day back from the long, long weekend! I hope you guys get this, its not the best, not 'hall of fame' material. It's okay, I just want this over and done with. So, PATRICK, your next scribe okay, make it a good one! =)

- CORRIE






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The reason we first multiply 200 by 12 is because the function is based on measurements in inches. In part (c) of the question you are asked to find the height when the wheel has turned:

(i) 15 inches
(ii) 100 inches, and
(iii) 200 feet. (There are 12 inches in a foot.)

This is an outstanding scribe post Corrie! Really well done. You've used colour in a meaningful way, your graphics compliment the text and you give careful explanations of what we learned in class today. So, for all that, your scribe post has been inducted into The Scribe Post Hall Of Fame.

Congratulations!

Hi Corrie,

A careful explanation and good graphics are the best! Congratulations your Hall of Fame post!!

Best,
Lani

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