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Monday, February 27, 2006

Today's pre-cal class was only in the afternoon during period 4.
Class started off with everyone anticipating for their test marks. Mr. K of course had not yet even seen the tests, so we'll have to wait and see.
Mr. K. talked about the Sunday activity, which was a game called "grow". Hint: dont't grow the ladder first or last. To beat the game we must eliminate possibilities.

Homework Quizzes
From now on their will be homework quizzes on anything we are assigned. You just simply copy the homework solution onto a piece of paper and hand it in. Textbooks will not be allowed, so you will not be able to actually solve the question during class time.

QUIZ
We had a quiz today on transformations, which was out of 10 marks.

Don't Forget
To do a post on blogging before every test to receive the 1 mark.

Transformations graphs:
* Follow the order of operations: B E D M A S


For the first graph, deal with the 3 by multiplying the x-coordinates by 1/3. Then shift your graph left 2 units.
RULE OF 3:

1) STRETCHES
2)REFLECTION
3)TRANSLATIONS

HOMEWORK:

chapter 1.6

Page 47 - every 3rd question up to and including 54




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Sunday, February 26, 2006

Let It Grow Sunday!

This week's game is called Grow.



Draw each item to the center of the ball to Grow it. If you drag them in the right order you will reach the maximum growth level for each object -- that's the challenge and it's not easy. ;-) Lots of trial and error. The number of different ways to play this game is 479 001 600. Can you find the winning strategy?

The Applied Math class will learn how to figure this out this week. Pre-Cal will learn it in about two more months and the AP Calculus students should remember from the Pre-Cal class. Do you?

Have Fun!



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Thursday, February 23, 2006

blog

this unit seems to be easy at first but as time pass by, it's getting more complicated. I had trouble in the pre-test with the b in y=asinb(x-c)+d. I don't know how to do it not until the end of that pre-test. that's the negative result of getting absent from the class. aside from that I think, like others do, the difficult part is getting the secant,cosecant and cotangent just from our mind. so, tomorrow is our first test. better be prepared for tomorrow because this subject will decide whether i'll graduate this year or not.



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Blogging for the test

Sorry if im doing this last minute, I've just had work for the past 2 days, so this was the only time I had to do this. Plus I really want to get a free mark on my test because im probably really gonna need it.
Ok, well the things I really struggled in this unit would probably have to be determining the sin, cos and tan values in the unit circle. Well actually just everything up to 2 pi, im okay with. Just the Values more than 2 pi I get confused by. Also what I had troubled in was the scaling of the x-axis in the graphs. I just get confused how you break up the scaling. I guess thats basically all I had troubled in. Well im gonna study now, good luck everyone!



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LUCKY SCRIBE # 13?!?!?!?!!!!




(un)LUCKY SCRIBE # 13,JEFFERSON REPORTING FOR DUTY!!!! Hiya. Today we had only one precal class today and today's lesson was quite, how you say,enjoyable. The fi rst half of the class, Mr k gave a brief explanations on the difference of functions and relations(gr 11). A function has one y value for every x value, however a relation has one x value for different y values. A function passes the vertical line test while a relation does not


He then explain that there2 kinds of functions or "flavors as how Mr K put it. One "flavour"(strawberry) has many(more than one) outputs for one input(2:1 function). For example:
y = x^2
f(-2) and f(2) = output of 4 there fore the out put is 4

The other "flavor(rocky road) has one input for one output. A 1:1 relation would be

y=x

Each input has its own output. Not every function has it's own inverse.

relations have many inputs for one output. Now here's the my favorite part where I understood what was happening. y = x has its own inverse ITSELF. Meaning the inverse doesn't look like it changed at all. I mean no coordinates or flips. Examples of theses are: y = cube root(x) and y = square root(x). If you want to see what the graph looks like, you can punch in the equation on the calculator.

Mr K then gave us notes to add into our math dictionary.(this will probably clear things for you and make it easier to understand)


Inverses: The inverse of any function f(x) is written as f^-1(x)


IMPORTANT!!!!!


F^-1(x) is read as : ”f inverse”
F^-1(x) “undoes” what ever f does


Example





Notice that the domain and range of a function becomes the range and domain respectively in the inverse


Numerically:


Given any ordered pair (a, b) from a function f, the inverse is found by exchanging the coordinates (b, a) in a table of values we simply Exchange the inputs and outputs.


Example




Symbolic(as equation)
To find the inverse of any function exchange the variable x and y, then solve for y (sqr = square root)
Algebraically:
y = (2x-3)^2
x = (2y-3)^2
sqr(x) = 2y - 3
sqr (x) + 3 = 2y
Sqr (x)/2 + 3 /2 = y
*note y = (2x-3)^2 and Sqr (x)/2 + 3 /2 = y are inverses


Conseptually:
We use the operations in a given function then write a second list, in reverse order of the inverse operations


Example:


f(x) = cube root(x^2 - 3)/2

1.square
2.subtract 3
3.cube root

4.divide by 2


f^-6
1.multiply by 2
2.cube
3.add 3
4.square root
F^-1(x) = sqr ( (2x)^3 +3)

F^-1(x) = sqr ( (2x)^# +3)
Graphically:


Given the graph of any function f we can find the inverse graph, f^-1 by reflecting f in the line y = x
Example: (solid blue line = line of reflection)

phew...that took me about 3 hrs on this scribe. It took my one hour for drawing the diagrams and 2 hrs typing up the math dictionary and read my mess of notes from Mr K's lecture and making the blog post nice and colourful =). I feel proud of myself because i've done one what looks like a good job from my perspective.Any ways its time for me to go STUDY HARD FELLOW STUDENTS!! REMEMBER WE WANT TO BE IN THE 80%+ RANGE!!

"MAY THE UNIT CIRCLE BE WITH YOU"

later days, Jefferson

OH YEAH. the scribe I pick next is the one who sits at the other end of the classroom, who? its Anh!!!!!




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Zaeneb: Blogging on Blogging Post

Zaeneb was having computer trouble. She emailed me her blogging on blogging post. Here it is....




On February the 10 it was a great class because I understood everything that we were doing in the class. And the most things that impresed me in that class was when every body was asking questions about the home work and the graphs witch I did not really under stood then I finally understood.

In the course I understood what the teacher was talking about the grasps and the other assignments therefore I did my home work and I was glad that everything was becoming clear to me.

The thing that I thought was cool is when the teacher had thought us the grasps. On doughty could make a big difference and a really nice grasp also we can make a hart beat.

the thing that I did not under sod is the graphs and how they work I did not know where to put the dots and how to get the droughts on finally I got it after so many explanations and dissociations about how they got it to be there and why it should be there the moment of clarification came when my friends described it to me and made it really clear to me why it should be there I hope that I will not mess the thoughts and do them wrong on the test.
No, I haven’t come across something in the real world or another class that we've discussed in class.



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Blooooog!

Truthfully, I am struggling in class, but not to the extent that I want to give up or that I tell myself I understand nothing. I can comprehend basically everything we've learned, but it takes me a little more time to let it sink in, so that I can use it and manipulate any given question with ease. I already know what can help me solve this problem; do more of my homework. I'm very aware that this was the case wit Mr. K's previous students near the beginning of the semester, and I really need to kick the habit of procrastination. So, all I really need to do in order to be at the classes pace, is to study harder.

I, specifically found that learning the values of the unit circle was no problem. Nor was solving trigonometric equations any hassle for me. I did have trouble with adding and subtracting fractions with different denomenators, but we already reivewed that in class yesterday, so I have a better understanding of that concept. As I've already stated, all I really need to do is put in more time into reviewing my notes and, as well as not sleep in class. Mr K, your class is awesome. You motivate us, make sure we're comfortable with the work, allow us to ask questions without hesitation and tell us interesting stories. In shorter terms, your class is fun and enjoyable. =)



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Wednesday, February 22, 2006

Scribe Number ? haha

Yeah yeah I know Marcquin probably doesn't have his scribe up yet so you're probably wondering why i'm scribing for today's class. It's simple he told me yesturday he was going to pick me. Haha talk about planning your future huh.

PERIOD 2
Well yeah I guess you can kind of tell that we had a double class today since i'm splitting what we did in both class (idea BORROWED from Teddie). Well during period 2 we were very fortunate, why you may ask because we had Ms. Ilagan (I think that's how you spell it ?) for half of the period and we did absolutely NOTHING =P. Just joking, Mr. K thought it would have been funny to leave us a FULL board of questions to do while he was gone "fooling around" with the junior highs during they're tour haha. I thought that was kind of mean because we could have used that time to help each other from yesturday's homework but no he deciding to be mean and leave us a review for our test on friday (BTW thanks Mr. K for that it helped PLENTY). And here's the questions:

a) sec π / 4 = 2 / root 2
b) csc π / 3 = 2 / root 3
c) cot π / 2 = 0
d) sec 7π / 6 = -2
e) csc 5π / 3 = -2 / root 3
f) cot (-3π / 2) = 0
g) sec (-3π / 4) = -2 / root 2
h) csc (-4π / 3) = 2 / root 3
i) cot (-15π / 6) = - root 3
j) sec (-24π / 3) = 1


NOTE: Red = answers just to clearify
btw they were in two columns on the board with a - e on side and f - j on the other.

Afterwards, we took the answers from the first column and either added, subtracted, mulitplied or divided it them with the question in column two.
Basically it was like :
a) + f) = 2 / root 2
b) - g) = 2(root 2 + root 3) / root 6
c) x h) = 0
d) / i) = 2 / root 3
e) - j) = ?? sorry I forgot to write it down but if you have it please tell me and i'll put it in

After all that we had 2 questions where we had to graph two equations:
a) y = -2cos3x+1
b) y = 3sin(x-π / 4) - 2
Sorry guys but I won't be able to put up the graphs for these functions because uhh I don't know how to make one that's easy to read =/, but if you would like to teach me that would be greatly appricaiated =D.

And the third question was to find two equations from a graph, a sin and a cosine.
The 2 equations where :
y = 2sin2(x-π / 4) - 1
y = -2cos2x-1

PERIOD 4
Second class started off rather strangely. Jessica told Mr. K that she had found a longer word than the one he had on the board (the left most board under the binary ( ones and zeros) code). She wrote it on the board and everyone tried to say it. haha To make it easier it was a lung diease from volcano dust =P haha you can ask Jessica what that word was if you really want to know it =P.

Anyway back on track, Mr. K started this class off with giving us examples to copy down in our dictionaries for transformations. One where it shifts on the y-axis, another shifts on the x-axis and a third where it does both. Then we went into the:

Streatches and Compressions
af(bx)

The Role of Parameter a
a > 1 The graph is stretched vertically by a factor a
0 less than a but less than 1 The graph of f is compressed vertically by a factor a
Essentially, a changes the y - coordinates of the function f
The y - coordinates are multiplied by a

The Role of Parameter b
b > 1 The graph of f is compressed horizontally
0 less than b but less than 1 The graph of f is stretched horizontally

Essentially, b changes the x - coordinates of the function f
The x- coordinates are multiplied by 1 / b
Mr. K then explained why we multiply by the recipricol of b, but I zoned out because he lost me haha yet when he explained it yesturday it made a lot of sense =/.

Again followed by a few examples showing the translations.

Then we started on our reflection notes :

Reflections
Given any function f(x) :
-f(x) : produces a reflection across the x-axis
The y - coordinates of f are multiplied by (-1)

f(-x) : produces a reflection across the y-axis
The x - coordinates of f are multiplied by (-1)

And that was the end of our notes. Mr. K then began explaining his baby clean up story with his daughter and related it to how inverses work (honestly Mr. K how do you find these relationships ? ) haha it was a really entertaining class today. oh BTW haha remember when you feel the bad feeling in you're stomach because of frustration turn the tv on and watch a comedy sitcom that's ONLY 30 MINUTES LONG. Why ? Because research shows that laughter relaxes the brain and something about connections happen ? haha so yeah enjoy.

Tomorrow's scibe is going to be dun dun dun J-E-F-F-E-R-S-O-N.



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Tuesday, February 21, 2006

Blah On Blahing

I'm hearing Blog way too often. Drives you insane eventually. Anyways, to discuss what I'm having trouble with, so that way Mr. K helps anyone or me. I have troubles with the following

Doing CSC and COT really fast and memorizing TAN.

That's about it. I'm working on it though. Just needed to post this. I need my marks =D



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blogging on blogging!

Today's class was fun for me because I was really understanding the concepts of this upcoming unit. To me, the stuff we're learning now is easy. This is maybe because we have already gone through the basics of graphs last year and a little bit this year. I am understanding many things throughout the first part of the semester, unlike last year where it was a struggle. The things that we're learning now are not new because we went over them last year. However, I'm having trouble remembering things that we have learned last year because it has been almost a year since I last took math.

An interesting thing that I have learned this year is how degrees is related to radians. This is the only thing that I can think of right now. I believe Mr.K said that it is easier to do problems in radians and now I can see why.

I was and still am having trouble with simplifying sin equations. At first when we were given sin(
π/4), I didn't know what to substitute into the bracket. Now that I understand it, I'm having difficulties doing the algebra behind it. Mainly it's when there are radicals in the equation. If you don't mind MR.K, I'd like some help so I can do better on these questions on the test. Another thing that I'm really having trouble with is when you have to apply the things we have learned into word problem solving questions.






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circular functions blog

This is my attempt of blogging on blogging. As of now we are done the circular functions unit so we are now learning a new unit, transformations. Today in class we learned how graphs can be either compressed or stretched and . If y= kf(x) where k is any real number and y= 2f(x) , then the graph is streched vertically by a factor 2. Also if y= 1/2 f(x) , then the graph is compressed horizontally by a factor of 1/2 In other words if k > 0 then the graph is streched by the factor of k and if k < color="#ff0000">k. If the value of k were a negative number; -2 or -1/2 the graph is not only streched or compressed but also is reflected on the x-axis.

I'm pretty confident about my knowledge in last course. I usually understand what is being taught to me. However it wasn't like that all the time, I was having a little trouble understanding the six basic trig functions. In attempt to conquer that weakness I asked a friend for help during a spare to find out that he also was having trouble in that section and we both ended up asking Mr. K for help, and yes we both understand it now. My favorite part of this unit would be the graphing because I find it easy to graph an equation and making up an equation for a graph isn't hard eaither. I think now I am prepared to write the test.

This is my picture of Pi;





Did you know there is a movie called "Pi The Movie" ? Well now you do. It appeared in the Sundance festival in 1998, directed by Darren Aronofsky. It is about a mathematical genius who is lost in his own world and is spiraling out of control. He is obsessed with explaining the essense of chaos theory. Critics said this movie was a thriller and a study of genius, obsession and madness. Cool?!? If you want to know more about it you can go to this link: http://www.pithemovie.com/gifpage.html (the official site for the film).



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Tell Your Parents the Blog is Multilingual!

You'll notice that all posts on our blog now have a series of flags automatically added to the bottom. Click on a contry flag to have the blog translated into that country's language. You can choose from:

French, German, Italian, Portugese, Spanish, Japanese, Korean, Chinese and Filipino

If you speak any of these languages, let me know if they work well enough to be understood. And tell your parents all about it! ;-) Encourage them to leave comments on the blog as well.



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Blog on Blogin'

I hope I'm in the right place for my post on blogging =/.

Well this is my post for the 1 mark on the test this Friday.

The other day, Mr Kuropatwa was reviewing how to graph sine and cosine graphs. He showed us how to get the new values for the graph by using the formula period=2Pi/B. The he started dividing it into halves, quarters and three-quarters. I don't know about the other students but I was very confused. So I looked at the new values for a long time and realized that if you took the reciprocal of B and multiply it by the original values, you will get your new values.

For example:

y=2sin4(x+5)+3
B=4, so the reciprocal would be, -1/4 (let's ignore the negative sign).

1/4(Pi/4)=Pi/16, 1/4(Pi/2)=Pi/8, 1/4(3Pi/2)=3Pi/8, 1/4(2Pi/1)=2Pi/4-->Pi/2

Therefore the new values for the graph of y=2sin4(x+5)+3 are:
Pi/16, Pi/8, 3Pi/8, Pi/2

This way of getting the new values for the sine and cosine equations has cleared things up for me. I found that it really helps in making it easy to find the new values to any sine or cosine graph. I thought it was pretty cool and it just clicked. =)



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Scribe #11

Sorry about the big delay on this, but I really tried my best to do this on time. I also apologize for falling asleep in class. That was pretty bad, but it was kind of funny that Marcquin had to poke me in the arm pit. Alright, so I, Jessica, was the scribe for YESTERDAY'S class. Yeah, I know I took long but I finished it!

Okay, so we had two classes, and in the morning Mr. K briefly addressed the class to get our blogging on blogging done. Why? Simply because the sooner we do it, he can help us with what we're struggling with, and we won't have such a hard time on the test on Friday. As we can see, what he said really did work. So Mr. K changed up what he had orginally planned out to do today [erm, I mean yesterday], and we worked on drawing sinusoidal graphs and determining the equation of a given graph.

We were given 2 equations to draw, which were:

y=sin2(x - π/2) +1 and
y=2cos3(x + π/6) -1

They ended up looking like this:



We were also given 2 graphs to find the sinusoidal equations of.

1.

This graph was determined as : y=3/2sinx

Technically speaking, there is more than one answer for any graph, and that there is an infinite amount of answers. This graph could've also been determined as:

y = -3/2cos3(x + π/6)
y = 3/2cos3(x- π/6)
y = -3/2sin3(x - π/3)


2.

This can be determined as y = 2sin π/2 +1 OR y = 2cos π/2(x-1)+1.








Then, in the afternoon, we were given a group problem to solve within fifteen minutes. Basically, you're on a ferris wheel that's 100 ft long, but you also must consider that the seat is 3 ft off the floor, so your maximum height would be 103 ft. It takes 15 seconds for one revolution and we were suppose to write this out as a funtion of time.

The answer we ended up with was f(t) = -50cos 2π/15 +53 OR f(t) = 50sin 2π/15(t-3.75) +50.

After that we copied some new things into our math dictionaries.

THE RELATIOINSHIP BETWEEN SINE AND COSINE




sinx = cos(x - π/2)
cosx = sin(x + π/2)

They are related by a phase shift of π/2.


UNIT 2 - TRANSFORMATIONS

Translations f(x - a) + b

The Role of Perameter a

*** [ NOTE: Where I've written in "is less than" just put < OR < in place of that. I wasn't able to use the "<" signs because it messed up the html coding and it looked all wrong. ]


a>0 The graph of f shifts RIGHT in a units
a increases the x-coordinates of f by a units
a [is less than] 0 The graph of f shifts LEFT in a units
a decreases the x-coordinates of f by a units

The Role of Perameter b

b>0 The graph of f shifts UP b units
b [is less than] 0 The graph of f shits DOWN
b units
∙The y-coordinates of f are changed by b units

And that's pretty much everything we covered yesterday. I know it's not immensly detailed, but I tried and hopefully it's helpful enough. For today's class, I chose Marcquin to be the scribe, so good luck with that.



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Monday, February 20, 2006

My Blog

Ok people it looks like we have finished our first unit in precal 4s. I think every thing is perfect. We have covered a lot of things in this unit and most of them I think are well understood. This is what we did for this unit:

We start off with CIRCULAR FUNCTIONS you know degrees and radians, and converting both using this equation D/180=R/pi. And I thought this was not hard, most of us understood it very well. The next thing we did is Complementary angles, supplementary angles, opposite angles, transversal, alternate angles, and corresponding angles. And this was well done for what I thought. Then there was arc length where we had this formulas R/2pi=L/2pir (for radians), D/360=L/2pir (for degrees), and R=L/r. This formulas where not that bad just take what you have and put it in the formula, easy. There was area of a SECTOR which was not that bad either. This time the UNIT CIRCLE which was hard on the beginning you know getting used to radians but then we did some mental math which helped us a lot. But then I still think that I have a problem when its big radians and - radians. But then I will get it one day. We did THE SIX BASIC TRIG FUNCTIONS and this was ok for most of us. And then the big one SINUSOIDAL FUNCTIONS. This most people had difficulties but I thought it was ok but then I had a some problems with the phase shift (C) but now I think I'm good with that after Mr. K helped us in today's morning class. Writing some problems on the board and we had to find the graph and then the 2 functions. Well that was it for this unit.

So you guys have fun and REMEMBER TEST ON FRIDAY.



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BLOGGER BLOGGING

I really liked today's class, even though half of the class was about something else. No matter, it was still related to math. It's actually amazing that Wile proved that "French dudes" theorem about having a higher integer power than two in the pythagorean theorem. Near the end i lost the point of why Wile was trying to solve the theorem, to see if it was actually true. Outstanding acheivements, like what Wile found out is remarkable. It makes you think, why didn't i think of that? Or i dont know what to say.

Mr. K, thanks for telling us about amazing people that did amazing things =). If we (students) work hard, more than just to pass, i think math will be more easier. The reward in the end...it's worth it.

I really feel good at this point in the course, the first unit had a mediocre difficulty. I get most of the stuff in class and this makes learning fun =p. There is one subject that i am confused about. reciprocal functions. i understand that i hae to reverse the values. What i am confused about is... Do we reverse exact values to find a pi value? Or do we reverse a pi value to find an exact value?

Learning how to graph funtions with a certain period also helped me. Before you showed us how to draw the graph, without squishing it into a small space; i did exatly that. i divided the area of 2 pi by what every value b was. I know how to graph a function more efficiently, when you showed us last week.

Well, that's all i can say for this blogging on blogging...

Bye world



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Surfing Sinefeld!

I found another π! It's getting closer .... ;-)

I'm getting lots of questions about graphing the trig functions -- keep'em coming folks! ;-)

I found something I thought might help. Play with Surfin' Sinefeld! He surfs sine graphs. ;-) (Click on the rectangle at the bottom with the word "graph" to start; and make sure your volume is on. Make sure to surf.) When your finished surfin' with Sinefeld, move on the the "Insidious Sinusoidal Quiz Device!"

OK, now lets play tag. I posted π, now it's your turn. When you post π you can also tag two people. The next two people to post π will be ........ Janet and jessica (I went with a J theme).



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Sisyphus' Bloggon the Blog 1

(Moved the post on to here from my own blog) 2/17/2006 05:11:00 PM

I honestly forgot we were getting our pre-test today, for marks! If I had remembered, things would be different. Well... not really, just an excuse. Today was a real learning experience for me, I really enjoyed the class. After we were done the test, we got into groups of three or four and went over the questions before handing them in. By discussing, and conversing about the answers made me understand a whole lot more. What Mr.K had said is true, "learning is a conversation." In our group, there was this one question where one of us had it right but we agreed on the wrong one! We made a few more mistakes, but it was just the little things that would've costed us marks half marks.

For example:

- I didn't check if it was correct in the given interval where 450 < x < 630 . Instead I just put a related angle answer 90 < x < 270, which was < 360.

- I found what the period was by looking from the origin, instead of the length in units between the max and min values which was 8. The period I thought was π/3, when thinking B was 6 all because I looked at it from the origin.

- When I labelled the graph I sketeched x and y for the two axis, but x was suppose to be time, and y was suppose to be P, as the question stated. Also there was a classmate that made quite the observation that Mr.K hadn't even seen, she said that time can't be negative, so it was only proper to draw a positive graph.

Next time, I'll remember to be more careful and aware of what the question asks. Good thing it was just a pre-test, because I'll make up for it on the real test. Here's hoping!


Blogging Prompt Response

"We've learned how to measure angles using both radians and degrees. Blog a brief paragraph identifing ways in which these two types of measurement are similar. Blog a second paragraph outlining the ways in which they are different. "

Both radians and degrees are related by being both a mesurement of angles. They were both made by mathemeticians and they are two of three modes found on a scientific calculator, with other one being graduates. By knowing an angle in radians, we are able to find out the what the angle is in with degrees, and vice versa.

Radians and degrees differ by how the angles are measured.
Radians is measured by taking the radius of a circle and using the length of the radius to wrap around the arc and coming back to the center point. This happens approx. 6.28 times for every circle, known as 2π, so half the circle is π (approx. 3.14).
Degrees is measured by the circle being evenly cut into 360, so there are 360 degrees in a circle, and 180 in a half circle. People came up with this concept because 360 has many factors in which it can be divided to evenly without remainders compared to other numbers.

π = 180 degrees = half circle
We can use this proportion to convert one angle of measurement to the other.


And, here's my Pi picture...





A Pi T-Shirt! Made out of 3.1415926...etc. Pretty cool. Gives me a brilliant idea of making a shirt with math formulas and going into it for a test. Imagine that, it'll surely help everyone.



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Test Bloggage

Hmm well this unit was pretty straight forward for me. Like the converting degrees to radians and vice versa sure no problem, and the arc length and the surface area of a sector easy stuff because it's like just plugging in the numbers to where they belong. Then here comes something like pi is an element of real numbers and graphing and i'm like uhh ? hmmm ? nothing's making sense. Well after today's class the graphing is beginning to make a lot of sense now. The break down of how it was supposed to be and everything really helped. Just a little more reviewing and practicing and this should be in the bag. Now when pi is an element of real numbers this is stuff I clearly have no idea of what is going on =/. I don't understand how it works and all that. But I will try to get it all understood by friday so I get into our agreed mark of 80 - 100 % =D.



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Post for Blogging on Blogging

Today's class was extraordinary from the days that we've been in the class. Personally, to tell you the truth doing the graph was really painful for me. Why? because I am not really a Math lover and it just come to a point in my head that it says "This must be STOP!!!" However, this day changed all my doubts in having to ever perform that such kind of graph. Seriously, I enjoyed this class today for what I've learned because of Mr.K continues effort but not that I'm saying that I don't enjoyed the previous classes that we had in the past, its just kind of different from today. Why? Because I'm happy to tell you that I understand it now, doing those graph is kind of EASY for me now. Unlike from the previous days that we were learning graphs, all I can say was "What was that?"or "Where did it came from?" Even though, I'm working those assignments that he gave us and almost every lunch, if I have time, I'm always asking for Mr.K's help.But I don't know it's just happen that it never got into my head. Maybe I'm not just fond with Math to get it into one sitting class.

Nevertheless my full thanks!!!to Mr. K for having such a GREAT PATIENCE for us. We all know that the party is just getting started but I hope this will continue this way.Well I guessed that's all I can say for our blogging on blogging.



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Sunday, February 19, 2006

Is this the blogging on blogging blog?

This better be the place. My head hurts from the word "BLOG" Anyways, I learned a lot about math since Mr.K is the type of teacher who talks a lot in class and explains the processes and definitions and all that jazz. haha whos says that? all that jazz. anyways, I remembered he taught us why there are 360 degrees in the a circle. No one really ever wonders that right. But he explained to us and it made sense. Something in my head clicked. No it did not explode. But it made sense all at once at the end of class. Sometimes I drift off when he talks. That shouldn't make him feel bad though. I do that to all my teachers (thumbs up)So far, everything makes sense and that makes me happy. Things coming to place and things I've learned that are serene in my mind make me feel dandy. Math is hard. It's the truth when you're the type of learner that's like me. If I could live with out math, I would, but then all them math lovers would find me in a mathematical way where there's a circle and I'm at the radius and they somehow make fire appear out of logical magic. But for now, it makes sense. The radians and arc lengths and all that jazz is pretty easy. And because of math, I'm losing myself in the logical world and straying away from the creative side that took over most of my soul. Darn you math. Oh. You can't use bad language. Sorry. At first, I found the memorizing of the unit circle extremely overwhelming. It even discouraged me from wanting to take math because of the UNIT ADLJFA CIRCLE. But in time, if you do your assignments, it just gets embedded into your memory and it seems like it's nothing at all. Listening and doing your work does benefit you. Who would have thunk it? I'm just rambling now so I'm going to stop. If you read this, you must have been extremely bored. Enjoy.



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BLAWGING ON BLAWGING!

Well well guys, it's that time. Where we students must make a post before a test(to get a mark on the test) on one of those selections that Mr. K posted on "Blogging on blogging". I choose to talk about my progress in precal 40s.
Honestly, it has been a bit of a bumpy road for the past 2 weeks for me. I was a bit intimidated on the work we had to do. But now I'm getting the hang of this course. I think?
I know how to convert radians into degrees and vice versa( I am confident I know how to do this!). I understand how to do arc lengths and sector of an area. However, I dont remember the formulas too well, but if i keep working on my questions ill remember them in no time =). No the trig functions, is really bumpy for me but i underestand the basics of it. Like "A" is the amplitude,"B" is NOT the period.,"C" is the phase shift(ie where the starting point of the graph will be), and "D" the sinusoidal axis.
Remember this: hard work DOES pay off =)(that means if you study really really hard, you'll get an awesome mark on the test on friday). Remember to study guys and "May the unit circle be with you." I know its out of season but look--->
its a pumkin pie GET IT!!!??hahahaha



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The Tenth Scribe

For the tenth scribe on the seventeenth day of February, Two-thousand-six... is me Mark.

Today was a half day and we had a pre-test for next weeks test. Even though this was a pre-test it was worth marks. The pre-test had about two questions i made mistakes and others in the classroom. Here are all the question that were on the pre-test:

1) Given sin y = (square root of three)/2, one possible value for y must be:

(a) 4 pi/3 (b) 2 pi/3 (c) 7 pi/6 (d) 11pi/6

Since y is positive, it must be lie in quadrant one or two. If you look at the answers: a, c and d they are negative sine values. B is the only positive sine value If you remember from the unit circle, 2 pi/3 lies in quadrant two.

2) The graph shown to the right is one period of f(x) = 3sin x. A second function g(x) is also shown. One possible value of x where these two functions intersect would be:


a) 3.87 b) 2.41 c) 5.55

d) 2.30

The first way to solve this equation is simple, using your graphing calculator. Plug in the equation f(x) and for g(x) plug in 2. Next, press graph. If we take a look at the graph the first intersection is around a value which is smaller than the choices given. So, press 2nd trace and then press 5 (intersection). move the cursor to the second intersection point, where g(x) and f(x) meet. The calculator says "first curve", all you have to do is press enter three times and the calculator will solve the intersection point. Finally the calculator gives you a value of 2.41.

NOTE: plug the equations in the "y =" window, like this:

y1 = 3sin x

y2 = 2

3) given cos (k) = -(square root of 3)/ 2, and 450o < k <>

cos (k) = -(square root of 3)/ 2

cos (k) = 5pi/ 6<<>

cos is in quadrant 2 and falls in our domain.

cos (k) must equal 150 degrees, but since our domain is between 450o and 630o, we get a value of 510o. How? add 150 degrees to 360.



4) A sinusoidal graph has a maximum value at (2, 5) and the next minimum is at (6, 3). What is the value of parameter B in the equation of this function.

We can find b easily, first plot the points on a graph and connect them together. Next, count the units (distance) from the first value to the second. You can subtract the y values. You should have a difference of eight. We can now find what the period is, since we have B.

period = 2pi/B

period = pi/4

Our answer, b = 8 and period = pi/4

NO CALCULATORS

5) The funtion P(t) = 100-20 cos 5pi(t)/3 approximates the blood pressure P in millimeters of mercury at time t in seconds for a person at rest.

a) Find the period of the function.

To find the period of the function we should rearrange the form of the equation into y = AcosB(x-C)+D:

y= -20 cos (5pi/3)(t) +100

B= 5pi/3

period = 2pi/B

period = 2pi/(5pi/3)

period = (2pi/1)(3/5pi)

period = 6pi/5pi

period = 6/5

b) Find the maximum and minimum value of the function

D = 100.and A = 20

Our maximum is 100 + 20, which is equal to 120

Our minimum is 100 - 20, which is equal to 80

c) Sketch a graph of the function show at least two cycles.

At this question, regine said to Mr. K that we are dealing with heart rate. Since we can't have a negative heart beat, our graph must have 2 positive cycles



Well that was the pre-test. For the actual test, there are links on the blog that you should try and practise. Also, the stencil that was given on thursday is due for Monday. Junior High tours will also be going on this week. Reminder: all people who signed up there is a meeting in Mr. K's room at lunch, on MOndaY?

Well that's it... o yea almost forgot. The next scribe is...eni meeni miny mo catch a tiger by the toe if he hollas let him go eni meeny miny mo... Jessica




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Chinese? Checkers? Chess?



Chinese Checkers it is called in England. Kinasjakk (Chinese Chess) in Norway. The truth is that it has nothing to do with neither checkers, chess, nor China.

'The Chinese Checkers game board is in the shape of a six pointed star and is playable with two up to six people at the same time. Each player uses pegs or markers of a different color placed within one of the points of the star. The object is to move all your ten pegs across the board (move one step at the time or jump over adjacent pegs) to occupy the star point directly opposite. The player getting all pegs across first wins.' - More.

You can play it here.

(Thanks again to Think Again!)



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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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π π Everywhere π


Wow! It's everywhere!

OK folks, now it's your turn. Everybody post π!

Hmmm...do you think there's such a thing as a π dance?

There is a Pi song! Kate Bush recently came out with a new CD. One of the songs on the CD is called Pi. Check out the lyrics.

There's even Pi music. Someone has managed to turn all the digits of π into the music of π! ;-)

Below you'll find several online quizzes you can take to prepare for your test next week:



Here are the answers to Exercise 6: page 1 of 3, page 2 of 3, page 3 of 3.



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Wednesday, February 15, 2006

scribe # ?!?!

First of all I would just like to thank michael for picking me as a scribe for today. I can possibly say that I am the luckiest scribe in the world.
Hmmm where to begin with all the knowledge educated to us today...ha
Mr. K was not at school today so we had a substitute, Mr. Ostrander, who was very benevolent to give us a period to do something productive or in other words a free period. Students were mainly working on their precal and or other homework. Now I don't know what else to share, I'm positive I've covered everything we did in class. So there is really nothing else to say except who the next scribe is. I'm choosing this person *ahem (T3DDiE) because he doesn't think he can handle it but I believe he *ahem (T3DDiE) will be able to execute it well tomorrow, so to not give out anymore hints *ahem (T3DDiE) I'm just gona say it, our next scribe for tomorrow will be T3DDiE!



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Tuesday, February 14, 2006

pi clock revealed? -- UPDATED

well apparently you cant put images on the comments, so heres my attempt on that pi clock question, the purple lines are shown as pi/12, it might be a little blurry, and the blue lines that i drew on the clock, were to pin point and assume that they were in the middle of the time indicated, enjoy..

click the picture to view, its ALOT better on the eyes



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Functions of Sin and Cos

Happy Valentines to all!! Sorry that this blog is just being posted now. I was having technical difficulties trying to figure this create the blog process. Unfortunately i was chosen to be the scribe when we had two classes. THANKS Emile. Just kidding and anyways let's get started with this blog.


Today we had two periods of math. Mr.k talked to us about PI Day. This special day occurs on March 14 at 1:59 and 26 sec. in the afternoon. Coincidently, it's the best time to eat pie.Mmmm. Also he told us about the coin hunt also happening on the same day. That was very funny how those teachers cheated their way into winning the hunt. Another event that was going to be going on is the math Carnival when the jr. high's come for their tours.

Today in class, we went over sine and cosine functions. The diagram below shows how each functions looks like.

For Sin,


For Cos,


The equation of the function is as follows: y= AsinB(x-C)+D


We only learned what D and A do to a graph. D is the sinusoidal axis or vertical shift or the average value of the function. Therefore, whatever the number substituted for D, it will be the y-coordinate of the imaginary line in which the function wraps around to. For example, if D was 1, the graph would like the diagram below.

In this diagram, the sinusoidal axis is at 1. Therefore it moved the function one unit higher.


Nextly, we looked at what A did to the function. We learned that A changes the amplitude of the function. In other words, the distance between the maximum or minimum of the function and the sinusoidal axis has changed. For example, if we were given the function, y=2cos(x), the diagram would look like the one below.

Lastly, Mr.K went over with us on what B does to the function. By plugging the information, y=sin(2X) into our graphing calculators, we saw that there were more waves in a given domain. In this case, there are 2 periods in the interval 2π. The diagram below will show the function
y= sin(2X).

The formula for finding the period of the function when given the equation is:

period = 2π/B

There is a short cut to drawing sin or cos functions when given a B value. Instead of drawing all those periods in the given interval, you can draw it like your basic function and just change the radians on the x-axis. The diagram below will give you a better understanding.


For the people who missed today's class, here's your notes. Finally I'm done!!! Hope you guys liked it.*YOU SHOULD, I PUT 2+ HOURS OF HARD WORK* Anyways. I have the honors of choosing our next scribe, who is........................................................................................................................................

........................................................................................................................................................................

.............................................................................................................................................Janet.


ps. Thanks Mr.K and Jackie for the help!!




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π Time!



π Day is Coming! The clock has started counting down! You can't tell from the picture, but the arms on this clock are moving in the mathematically correct direction: counterclockwise.


Pictures like this always get me wondering.....


Blogging Prompt
  • What π time is it? (state exact hours, minutes, and seconds in radians)

  • How much longer do we have to wait (in radian hours, minutes and seconds) until it's π (pie?) time?




Ok, let's have some fun with this.....can you find and post pictures of π? This one is an actual sculpture in Seattle. Can you find π in nature? Lets see how many pictures we can find. ;-)


Happy Blogging!



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Monday, February 13, 2006

Sticks and Shadows

What's the connection between circles and triangles? That's what we've been talking about in class.

Trigonometry has something to do with it. I found an excellent site that allows you to play and learn all about it. Start with Stick and Shadows Part I and play through to Frequency and Amplitude.

Tomorrow we're going to talk about how to graph the sine, cosine and tangent functions. You can do a little preview here.

If you review this material before our class tomorrow you'll find class really easy to follow.

And, finally, as promised, the answers to Exercise 4 (page 1 of 2, page 2 of 2) and Exercise 5 (page 1 of 2, page 2 of 2).



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Lucky Scribe

Hi! Guyzzz... This is Emile your sixth scribe for the wonderful Monday of February.I hope I can explain this to you smoothly.

Alright, let's get into the business.It's an even day today so we only have an afternoon class.To start with, Mr. K gave us some problems to solved as follows:
1.cos2x+2cosx=0; First you need to common factor it,
cosx(cosx+2)=0;there are 2 possible answers...
a. cosx=0( in radians are:3pi/2 and pi/2)Why? Because the cos theta is equal to zero in those radians.
b.cosx=-2 which is we all know that undefine because the highest value cos can have is 1 and the lowest value is -1
2.2sin2x+sinx=6
2sin2x+sinx-6=0;then
(2sinx-3)(sinx+2)=0
a.sinx=3/2 b.sinx=-2
This two have No solution because 3/2 is bigger than 1 and -2 is smaller than -1.
3.2cos2x=7cosx-3
2cos2x-7cosx+3=0
(2cosx-1)(cosx-3)=0;There are 2 possible answers
a.cosx=1/2 which is pi/3,5pi/3,7pi/3,13pi/3 etc.
b cosx=3 undefine
4. tan2x-1=0
(tanx+1)(tanx-1)=0
a.tanx=-1 which is 3pi/4, 7pi/4 etc.
b.tanx=1 which is pi/4,5pi/4 etc.

BUT, Mr. K trick us realizing that if we do that on the exam we're going to lost half a mark.Why?Simply because we don't have enough answer for those type of questions.We should notice that on exercise there was no specific domain that he gave us, so that means we just continue to give an answer but... he taught us some shortcut to do this kind of thing.Like:
1.Instead of writing many answer you can just write:
x=pi/2+kpi;let k be the integer
Since number 2 has no solution we'll just leave it like that
3.Instead of writing many answers you can just write for:
a.x=pi/3+2kpi; let k be the integer or
x=5pi/3+2kpi; let k be the integer
4.Like the others:
a.3pi/4+kpi; let k be the integer
b.pi/4+kpi; let k be the integer

After those problem solving we did another MENTAL MATH about the unit circle, which I think we're doing fine.Then we end our day by answering some questions from Ex.4. Don't forget that we have an assignment in Ex.5.

Well, I guessed that's it for me.Until your next scribe, who is Michael.



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Sunday, February 12, 2006

Sunday Funday!

Each Sunday, just for fun, I will post an online game or puzzle. This week it's a logic puzzle ... we look in on a prisoner with a problem ....




For the last trial, the king used not two, nor three, but nine rooms! The prisoner was told that one room contained a Lady and the other eight were either empty or filled with a tiger. The sign on the Lady's door was true, the signs on room with tigers were false, and empty rooms had signs that were either true or false.

These were the signs:

  1. The lady is in an odd-numbered room.

  2. This room is empty.

  3. Either sign 5 is right or sign 7 is wrong.

  4. Sign 1 is wrong.

  5. Either sign 2 or sign 4 is right.

  6. Sign 3 is wrong.

  7. 7. The lady is not in room 1.

  8. This room contains a tiger and room 9 is empty.

  9. This room contains a tiger and 6 is wrong.


The prisoner studied the nine signs for a while and came to the conclusion that the problem was unsolvable. The king admitted his mistake and told the poor prisoner if room eight was empty or not.

The prisoner needed no more help. He deduced where the Lady was. What about you?

Problem source: The Lady or the Tiger and other Logic Puzzles by Raymond Smullyan. (With thanks to Think Again!)



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Saturday, February 11, 2006

Scribe Time!

Well I just want to start this off by saying sorry guys for the late scribe.

Anyways lets get right into it,
We started off the class with Mr. K giving us 4 questions (questions that we should all know how to do by now), where we had to solve for x:


Answers are as follow:
1. x= 1/3 2. x= 0, 1 3. x= -6, 1 4. x= 1/2, -1

But of course there was a catch to these easy questions, which led to the next lesson.
Mr. K then gave us 3 more questions:

1. 3cosx + 1 = 2
2. sin^2x - sinx= 0
3. tan^2x + 5tanx= 6

Okay, now we're all thinking what the heck is this, but it is actually easier than it looks. We solve this like how we've been always solving equations. Except once we get to the last line, where we're trying to solve for x, we use our 2nd function on our calculator and the function sin or cos or tan, to get the actual value of x. In other cases, we dont even need to use our calculator to find the value of x. Confused?!? Okay let's take a closer look at it.

Heres a case where we dont have to use a calculator to find the value of x:


Heres another easier way of solving these types of problems:


After looking at those questions, we did 2 quizzes to help us learn the unit circle more. Then after lunch, Mr. K gave us more questions just like the previous ones. For people who weren't in class, here they are for practice sake.

1. Cos2x + 3cosx + 2 = 0
2. 4 sin^2x - 1 = 0
3. 3tan^2x - tanx + 4 = 0

Answers are:
1. x= no solution x= 180 degrees
2. x= 7 pi/ 6 , 11 pi / 6 x= pi / 6, 5 pi/ 6
3. No solution

Then we went over some homework questions people had troubled on, then Mr. K gaves us 2 worksheets that we had to solve in a group, and hand in for marks.

Oh yeah for people who weren't in class we took down some notes also.


Okay well thats pretty much all I can remember guys, sorry it couldn't be anymore longer and again sorry for the wait.

The next sribe for monday is Emile.



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Fundrasier

Hey guys you probably have or have not heard about this event that we are holding at our school next month in march. Well it's a funraiser for War Child called "Keep the Beat." It's basically like a dance off for all the "B-Boying" and Hip Hop dancers out there. Futher details about this event can be easily obtained by your very own president or your vice president. OH btw did I mention it's open to everyone ? Yes everyone, meaning people outside our school doors who just love to dance, so make sure you guys tell all your friends so we can have a great turn out for this event.

BTW if you guys haven't noticed yet, it's almost PI day (nearly a month away), and that means the coin hunt is going to be starting soon. Be on the look out for March 14 (PI) for which this event is going to begin, and if you want any further details on that you can easily ask Mr. K. It's not as easy as walking around the school with a magnifying glass walking around and searching every square millimetre of the school. It's about figuring math problems, hence Mr. K thought of it. =P

Hope you guys try to help us out in supporting our school with these two events happening in the near future.



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Thursday, February 09, 2006

Scribe #4: Circular Functions

Beautiful day, beautiful day, here in Winterpeg, Manisnowba. This is Manny doing the scribe for today! I'll try to make this as short and concise as possible, because I'm just a straight to the point kind of guy. Well let's get down to it then.

Today in class we got a surprise, quiz on circular functions (out of 16 marks). It wasn't too bad, there was nothing new, it was just the stuff we've been doing all week long.

The quiz consisted of 4 parts:
1)
Convert to Radians
2) Convert to Degrees
3) Determine the Quadrant of a Radian given
4) Determining a coordinate on the unit circle given a coordinate outside the unit circle.

The toughest part of the quiz that a lot of people had difficulties on was the last part. The question went like…

“Assuming the point P lies on the intersection of the unit circle and the line segment joining the origin to the point Q(-9, 40) find coordinates of P.”

Here’s how what the diagram might look like if you were to draw it:

Well, how I tackled the question was stating what I know.
- On the unit circle, the radius, which is the hypotenuse in this case is always equal to 1.
- The coordinate Q(-9,40), is expressed as (cosine, sine), because cosine runs along the x-axis (horizontal distance), and sine runs along the y-axis (vertical distance).

Therefore, cosine = -9 and your sine = 40.

So you now need to find your hypotenuse, and when you find your hypotenuse you can reduce that value to one by dividing whatever number it may be with itself. When you do that, you must divide your cosine, and sine by the same number of what the hypotenuse was in order to not change the value of anything.

With the Pythagorean Theorem you can find your hypotenuse because it is a right angle triangle.
h² = cos² + sine² where h is your hypotenuse
h² = -9² + 40²
h² = 81 + 1600
h² = 1681
h = 41

So by dividing the hypotenuse by itself will get you the value of 1 which is on the unit circle, and you must now divide all other values by the same number in order for it to remain the same value.

So on the unit circle, cosine = -9/41 and sine = 40/41
Therefore the coordinate would be P(-9/41, 40/41)

During the quiz to those who were done, Mr.K wrote up some brain stumpers (well to me anyway) on the white board to pass the time. I’m usually bad with puzzles, I only got the first one =(. It kind of looked like this.

Can you draw these pictures without lifting your pencil and crossing any line?

Well back on topic, after everyone was done the quiz, we switched papers and marked. Apparently there are many provincial rules on marking, which can cost you many marks and which applies to us.

Some of the rules I remembered are:
- always reduce to lowest terms
- don’t have a train of “=“ signs
- follow what the question says, e.g. round of to nearest tenth, so if it was 3.43, it would be 3.4, not 3.43
- make sure you have the variable in which the answer is equal to, don’t just drop it (I have a tendency to do this one), e.g.
x= 10/2
= 5
(wrong) x = 5 (right)

These are a few mistakes we tend to make by not following certain rules, and from now on it’ll cost us marks! So always be on the look out for these little mistakes.

Then we went over some problems that some of us had difficulties on, in our homework assignments. And then it was the end of class. Whew… I tried making it as short as it could be, but it seems like I can go on and on. Sorry if none of it made sense to anyone. If it didn’t you can ask me to explain it to you in person anytime, and I’ll try my best to. And no homework for today! So celebrate while you still can.

Oh and, if anyone has a few ideas or suggestions on how to convince Mr.K to let me move from the front row seat to anywhere else, let me know and I’ll give you candy =). Like Sisyphus I’ll never give up. It’s just too bad Mr.K has the same attitude. But he’s playing more a role of Hades in this case scenario, where he’s putting me in a spot for like forever and will never let me leave from it. *Sigh...

Well it’s been fun being the scribe for today, now, next on my list of priorities… food.

And, I almost forgot! The next scribe is Jacky S. Why? Just because I can…=D




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Wednesday, February 08, 2006

The Scribe List

This is The Scribe List. Every possible scribe in our class is listed here. This list will be updated every day. If you see someone's name crossed off on this list then you CANNOT choose them as the scribe for the next class.

This post can be quickly accesed from the [Links] list over there on the right hand sidebar. Check here before you choose a scribe for tomorrow's class when it is your turn to do so.

Cycle 4
calvinw.
Jacky S.
a-b33-l
Abdi
aldridge
Manny
Emile
Jefferson
Regine
Van
michael
MARK
marcquin**
jessica
janet
T3DDiE
jan
Anh
Lerwyne
senait*?
raymond?
charlene



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Trigonometry Meets Geometry

As promised, you can "see" the sine, cosine and tangent functions represented geometrically here. Click on the yellow dot and drag it around the screen.

Also, you can download the answers to Exercise #2 (Page 1 of 3, Page 2 of 3, Page 3 of 3) and Exercise #3.

Have fun playing with that applet! ;-)



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Scribe #3

Hi guys this Abdi if u don't know me and today I'm the scribe. We had 2 classes today. On the morning class which is period 2 we started off with Mr. K writing some problems on the board and we had to solve them.

Questions:

1. Find the coterminal angle for:
a) -45 degrees b) Pi radians c) 240 degrees d) 10Pi/3 radians

2. Convert to degrees:
a)4.21 b) 11Pi/3

3. Find the missing side and the value of Sin. of theta, cos. of theta, and tan. of theta:
a)




b)



Answers:

1. a) 315 degrees b) 3Pi or -Pi and more c) -120 d) 4Pi/3, -2Pi/3, 16Pi/3, and more.
2. a) D/180 = R/Pi
theta/180 = 4.21/Pi
theta = 757.8/Pi
theta = 241.2152 degrees
b) D/180 = 11Pi/3/Pi
theta = 11Pi/3 * 1/Pi
theta = 1980/3
theta = 660 degrees

3. a) 8 square = 4 square + X square
64 = 16 + X square
square root of 48 = X
4 square root of 3 = X
sin. theta = 4/8 = 1/2
cos. theta = 4 square root of 3/8 = square roof of 3/2
tan. theta = 4/ 4 square roof of 3 = 1/square roof 3 * square 3 / square 3 = square roof of 3 / 3

b) sin. theta = 5/5 square root of 2= 1/square root of 2 * square root of 2/square root of 2 = square root of 2/ 2.
cos. theta = square root of 2/ 2.
tan. theta = 5/5 = 1

Well that was all we did for the first class, now second class which was after lunch.



black : 2Pi (1,0)
Pi/2 (0,1)
Pi (-1,0)
3Pi/2 (0,-1)
blue : Pi (square root of 3/2 , 1/2)
5Pi/6 (-square root of 3/2 , 1/2)
7Pi/6 (-square root of 3/2 , -1/2)
11Pi/6 (square root of 3/2 , -1/2)
red : Pi/4 (square root of 2/2, square root of 2/2)
3Pi/4 (-square root of 2/2, square root of 2/2)
5Pi/4 (-square root of 2/2, -square root of 2/2)
7Pi/4 (square root of 2/2, -square root of 2/2)
green : Pi/3 (1/2, square root of 3/2)
2Pi/3 (-1/2, square root of 3/2)
4Pi/3 (-1/2, -square root of 3/2)
5Pi/3 (1/2, -square root of 3/2)

tan.

black : all undefined
blue : 1/square root of 3
-1/square root of 3
1/square root of 3
-1/square root of 3 (respectively)
red : 1
-1
1
-1 (respectively)
green : square root of 3
-square root of 3
square root of 3
-square root of 3

Biggest size of cos. You can get is 1 and smallest size is -1. Biggest size of sin. you can get is 1 and smallest size is -1.

anyways that was all for the scribe and let me tell you guys something, it was really hard to explain this and it took me hours to do this and I know its not the way you guys expected but this is the only way I could do. So if u guys have anything to say to this please leave me a comment and I will try to fix it. So the scribe for tomorrow will be MANNY.
GOOD LUCK AND U ALL HAVE FUN.



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Tuesday, February 07, 2006

Day 2 Scribe

Hello fellow students, my name is Calvin. This is the 2nd scribe, we're well on our way for our " book " ha. well lets start....! I cannot guarantee that following information is accurate.

Okay so in the morning we didn't have any classes because it is a even day. We started our day in the class of Mr. K, as he explained a little about "Blogging on Blogging" which is now posted for your enjoyment. He introduced us a new way of taking care of homework questions that we as the students didn't understand or didn't get. In order to get help on these questions, as you walked in the class, there would be a person standing beside the side board in the room, which would be putting checks beside the questions that you needed assistance with. The person who volunteered to do this task was our brave Janet.

We received handouts, which included Exercises' 2-6, along with the answers to the first exercise. The answers for exercises 2-6 are on this web blog somewhere... I think? We have a new student in our classroom, his name is Jan. I believe he will need some assistance with what he missed, any volunteers? Don't look at me... =P Okay well we began on our Math Dictionaries.

Standard Position - The line starting at the 0° to measure an angle anywhere in the circle.

Transversal - The line that goes through 2 parallel lines.

Sector - Two radius lines that make an angle. ( eg. a slice of pizza )

( These defininations are my own words, just my way of making them seem simple opposed from Mr. K's line of fanciness )

As the class comes near to the end of the period, we learn a new formula to calculate the " area of sector "

         In Degrees                     In Radians

           θ          S                       S         θ                      θr²
         ------ = ------                ------ = ------    OR    S = ------
         360°       πr²                   2π       πr²                     2


θ is the angle in degrees or the angle in radians
S is the area of the sector
r is the radius

Example :

Find the Area of the Sector with central angle of 30° in a circle with the radius of 10 cm

                30°            S
               -----    =   -------
                360          π(10)²

      30 - 100π
      ------------    =   S
           360

               25 π
              ------    =   S
                 3
      26.1799 cm² ≈   S

                          ^
Note that, that is NOT an equal sign, it represents that it is approximately that value.

To finish this off, we drew the diagram of the unit circle, labeling the main angles which were mentioned earlier that day and posted by Van. *Refer to the previous scribe for the angles which you WILL have to remember. The class had ended early because of the early dismissal, hope this was insiteful enough for you bloggers out there.


Eck this stuff really does take long, good luck to the next scribe, Abdi. Good luck, please make it more interesting than my own.
** Information maybe not accurate, as it was my take on the flow of words coming out of Mr.K's mouth. **

                            © of Calvin Incorp. 2006



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