## Wednesday, February 28, 2007

### TODAY ,TODAY

First thing we kinda went over today was an efficient way to graph our functions and their reciprocals. As the first slide of today's class shows is an order that we can use in order to help us graph. Also Mr.K said that you don't necessarily have to follow that order but should do so always with #1 and 2.

- Number 1 on the table that was shown to us was to find the variant points which is in when y equals 1 or -1 on the graph drawn.

- Number 2 on the table was to find the asymptotes, which was when y=0 on the x-axis on the drawn graph. Where the asymptotes are on the graph there must be a dotted line .

The order in which you do the other steps doesn't matter.

Sorry my dots are hard to see but there are two blue dots at the variant points and the red circle is where the asymptote is located.

Step2: The asymptote is on the line x=0 so that is where the reciprocal graphs cannot touch

Step3: from the variant point to the asymptote on the left side of the graph the y coordinates are biggering negatively so on the reciprocal graph they are smallering negatively.

from the variant point to the asymptote on the right side of the graph the y coordinates are smallering so on the reciprocal graph they are biggering.

Step 4: from the variant point on the left side of the graph to infinite the y-coordinates are biggering negatively so on the reciprocal they are smallering negatively

from the variant point on the right side of the graph to infinite the y-coordinates are biggering so the reciprocal y coordinates are smallering.

x²+1 which is f(x)=1/x²+1

To Find more about Ms. Angesi

Funny thing she told us to make sure we have all our credits and that they are all counted for b/c I actually went down to the guidance office and I was missing a credit I earned in grade 9 when I came from the U.S. well that's all folks. Not a long post huh? sorry and the next scribe is .......drumroll........jann.

Bye guys

### Today's Slides: February 28

To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

## Tuesday, February 27, 2007

### ex 10

### The Time Has Come...

...anounced after my scribe

**Morning Class:**

Our class started off without me there unfortunately, but none the less it went on anyway :'(. Mr. K and the rest of the class was praising Chris' amazing scribe, ( thanks for setting the bar really high for the people who have never done a scribe before). Also Danny had been choosen to be scribe for the day, and i heard he was crying. luckily KADEEM SAVES THE DAY! and arrives late, after Sandy and Albert, but prior to Miles.

Back to business. Mr. K started us off with 10 questions, with the first 5 we were given a function y=f(x) and a point on the graph (-2.-3) and told to find the coordinates of it's image on the graph.So basically what your doing is finding the X or Y coordinates using f(x).

Here's a few examples:

**y=f(x) + 2**--> shows this function being translated up 2 units, so the original point (-2,-3) is moved up 2 units, giving us a new point at

**(-2,-1)**

**y= f(x+3)**--> shows the function being shifted to 3 units to the left (8)"to the left, to the left"(8). Ha ha. so you use the point (-2,-3) // (x,y) and put it int he function giving us the point

**(-5,-3)**

If your not understanding that lets just put it this way:

*****REMEMBER STRETCHES BEFORE TRANSLATIONS*****

OK let's say the original value was (-2, -3) for example. Ha ha ha. First you add the X value to the coordinate than you do the same to the Y value and you get your answer. Remember ADBC. (Stretch, translation, stretch, translation). First you check if f(x) has any stretches and multiply accordingly, then you add/subtract to figure out the location of the x/y coordinate.

The next set of questions Mr. K assigned we were given the final point of the functions prior and told to find the original function.

For example:

Function: y=f(x+3) Final Coordinate: (-3,7) Original Coordinate: (0,7)

When your trying to figure out what the original coordinates were, first of all you have to add/subtract the stretches or else the answer will be wrong, then you multiply/divide to figure out what the original coordinates are. For example if you have the coordinates (3, -2) and are using y= f(2 ( (x+1) + 2 you first have to use translations to find the X and Y values before the stretches, in this example that would be (4, 0) and then you use stretches dividing/multiplying to figure out what the final value is which is (2, 0).

The Next thing we learned was:

**Even and Odd Functions**

Even Functions

**A function is "even" its graph is symmetrical about the origin**

or

IFF (If and only if)

**(**f(-x) = f(x)

**)**

f(x) = x²

f(-x) = (-x)²

f(-x) = x²

Since f(-x) = f(x) the function is even

**Odd Functions**

A function is odd if you are able to rotate it 180 degrees and it would be the same graph

or

IFF f(-x) = -f(x)

ex.

f(x) = x³ - x

f(-x) = (-x)³ - (-x)

f(x) = -x³ + x

Not an even function

-f(x) = -(-x³ - x)

-f(x) = x³ + x

Since f(-x) = -f(x) the function is ODD!

There is a few more examples of these even and odd examples in Mr. K's slide posted today and in our exercise ( go over them and practice it). So that's was the end of our morning class... all i can remember was my head spinning.

**Afternoon Class:**

The afternoon class, i knew what was expected of this class already since Mr. K said he would be leaving half way through the class, but not until he taught us this reciprocal thing, and you know what that meant (rush and cram) but fun, and this is what we learned:

We found the reciprocals of the following numbers:

**DOCTOR SUESS' PRE CALCULUS CLASS**

1 2 4 10 100 1000 1000000 0.5 0.25 0.1 0.01 0.0001 0.0000001

then we found the reciprocals of...

-1 -2 -4 -10 -100 -1000 -1000000 -0.5 -0.25 -0.1 -0.01 -0.0001 -0.0000001

- As the positive numbers got bigger their reciprocals got smaller, and as the numbers got smaller their reciprocals got bigger
- As the numbers were "biggering negatively" their reciprocals were "smallering negatively" and as the numbers were "smallering negatively" their reciprocals were "biggering negatively"

The Graph shown above is (x+2) and its reciprocal 1/(x+2)

the purple circles indicate the invariant points. The invariant points are points that don't move on the graph,the points where the function and its reciprocal meet/touch.

As you can see if the function is biggering negatively, the reciprocal is smallering negatively and vice-verse.

And last but not least how to draw the reciprocal when you know the function already, you can see it here.

So all though we've come, to the end of the road, i am so very excited to let go. I'm sorry my scribe went up so late this honestly was the hardest thing I've ever done and it's still pretty bad because i am now half asleep haven't even gotten to study for my AP Chemistry test tomorrow. With that said, tomorrows scribe will be...

Lauressa Lauressa LauressaLauressa Lauressa Lauressa Lauressa Lauressa Lauressa Lauressa Lauressa Lauressa asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL asseruaL

### Today's Slides: February 27

To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

## Monday, February 26, 2007

### Lost in translation...and stretching.

__Friday Morning:__

I was not in class on Friday morning, as I had to go to "Doors Open," an extracurricular program for history class. But despite my absence, I asked around and determined that we didn't learn anything in the morning. All we were told was that exercise nine was assigned for homework over the weekend, but we weren't taught about stretches yet so we could not complete the exercise. So basically, the entire class was spent working on other subject work or "working" on the smart board. Nothing new was learned in this class.

__Friday Afternoon:__

I was present for the afternoon class, but then again there really wasn't any point to be there. We again didn't learn anything or accomplish any work, so we were either completing work concerning other subjects or (as the majority of the class did) played hangman about "math" on the board. Yeah...that was the main topic...math. Well, that was what the afternoon pretty much consisted of. But now on to where the most recent information that he taught us.

__Weekend:__

**A summary of the movie:**

y=-f(x) <-- This function will be reflected over the x-axis, as the negative value is changing the y-values of the function. That negative sign is -1, so if you multiply all y-values by -1 the graph will appear to be flipped over the x-axis.

y=f(-x) <-- The same fits for this function, but it will be reflected over the y-axis. The negative 1 is multiplied by all the x-values of the function, causing them to be flipped horizontally over the y-axis.

He then ended it by saying that inverse functions will be explained in class, which was later proved to be true.

__Monday's Class:__

Today's class, we learned a lot useful and very interesting information about our new unit. I came into class and I saw that Mr. K had the aforementioned video up on the smart board, and I naturally assumed that we were going to go over it. This was true. So we began the class by watching the video, as much of the class did not get to watch it over the weekend. He paused the video at certain points and elaborated upon and fixed what he said in the video. The first time he paused it was to explain stretches and compressions.

When the function y=f(x) is altered by adding a value to multiply the output, in the case he showed us, y=2f(x), we can find the new y-values of the function easily. The 2 in front of the function alters y-coordinates, so all we must do is multiply the y values in the original graph by 2 to find the new functions y-coordinates. This causes a vertical stretch, and he showed this stretch by using the following graph:

The red line represents y=2sin(x).

The graph shows how once the graph was transformed by multiplying all y-values by 2, the graph was stretched vertically. But if the value is decreased, say to less than 1, such as 1/2, how will the graph look?

In the graph, the transformation is compressed vertically, which shows what happens to the y-values of the original function when the output is multiplied by a number less than 1. The graph becomes compressed, and the y-values are multiplied by, in this case, 1/2, which causes the new function to have lower y-values, causing it's compression. But this is not the only type of stretch that he showed us, as he also showed us horizontal stretch.

The graph now shows y=sin(x) compared to y=sin(2x). The graph is compressed, and Mr. K went in depth into his explanation of why this is. He explained that:

- In this case, you're doubling the input before it was calculated by the sin function. Before you do this, you multiply the x value by 2, doubling the original value before you find the sin.
- This makes the function happen faster, as you're multiplying the value before it is input into the function.
- To determine the x-values of the transformed function, you multiply all x-values by the recipricol of the value. In this case, to find any x-coordinate in the new function, you must multiply the original functions value by 1/2.

**doubled.**The graph is stretched horizontally, and as detailed before, to find the new x-coordinates of the transformed function you must multiply the original values by the recipricol of the value.

Each of the above graphs help portray how functions are stretched and compressed and then once we were shown all of these graphs, we were given a general equation to represent these parameters. In general we see:

**y=af(bx)**

The value of

**a**represents the vertical stretch of the functions transformation. The value of a is used to multiply the y-values of the original function to find the new function.

**A**alters the y-values of a function.

The value of

**b**represents the horizontal stretch of the functions transformation. Though, the value of

**b**is not the value used to determine the new function's coordinates, we must use the reciprocal of

**b**. We must do this since

**b**alters the values being input into the equation before it is actually calculated. For example, in the function y=sin(x), the transformation of y=sin(2x) causes the values of x to be doubled

**before**it is calculated into the function of sine. In order to counteract this, we must use the reciprocal so that the values will end up equivalent before going into the sine function. In this case, if x=Î /2.

**b**is not what we're multiplying our x-values of the original function by, we're multiplying by the reciprocal.

Then we partially reviewed translations from previous classes:

**y=f(x-a)+b**

The value of

**a**represents the horizontal slide of the function.

- If
**a**is greater than 0 then the function is shifted to the right**a**units. In this case, the x-coordinates increase. - If
**a**is less than 0 then the function is shifted to the left**a**units. In this case, the x-coordinates decrease.

**[Don't forget to pay attention to the sign of (x-a)]**

The value of

**b**represents the vertical slide of the function.

- If
**b**is greater than 0 then the function is shifted up**b**units. In this case, the y-coordinates increase. - If
**b**is less than 0 then the function is shifted down**b**units. In this case, the y-coordinates decrease.

After we finished reviewing translations, we then worked on graphing some of these newly taught stretches and compressions, as well as translations. He showed us a graph on the smart board, and then we had to alter it accordingly. These questions can be found on slide 2 here. The last question was composed of both stretches and translations, and from this question he taught us an important rule:

**[Stretches come before translations]**

Always work out stretches before translations. Well, now that all that was done, he quickly taught us about inverse functions.

He began by outright telling us that an inverse undoes whatever has been done to something. He then contrasted this to the "inverse" relationship between his daughter and his wife and himself. Every morning, his daughter goes into her clean room, then she transforms the room into a messy room. At night, the super inverse parents come into the messy room to clean up the mess, and trasnform the room **back** into a clean room. He showed a diagram of this:

Then we went more into the work involving the inverse function. The -1 above the inverse function's F does not mean it's to the exponent -1, that would be written as [f(x)]^{-1} . An inverse function "undoes" the transformations of a function through a routine, and the function of a regular function switches y and x values.

f --> f^{-1}

(a,b) --> (b,a)

If you consider Mr. K's example, the messy room is the domain of f(x), and the clean room is the range. In other words, in the function f(x), the messy room represents all the x-coordinates, while the clean room represents all the y-coordinates. In the inverse of the function, however, we switch the messy and clean rooms around. By doing this, we're switching the domain and range around, which is exactly what happens in an inverse function.

(a, b) = (messy room, clean room)

(b, a) = (clean room, messy room)

He then showed us the inverse function of f^{-1}(x) through different methods.**Algebraically**

The inverse of a function can be determined algebraically. In the equation, switch the x and y variables, then solve for y to receive the naturalform of a function. We must due this so that we can graph it. Consider the function f(x).

f(x) --> y=√2x^{3}-4

f^{-1}(x) --> x=√2y^{3}-4

x^{2}=2y^{3}-4

x^{2}+4=2y^{3}

x^{2}+4=y^{3}

y=√((x

^{2}+4)/2) <-- we are now able to graph this.

**Conceptually**

We can also display the inverse of a function by undoing whatever has been done to the function. Whatever order is taken to transform the function, the inverse will undo these transformations by reversing the order and reversing the operations. An example is shown in here on slide 3.

**Graphically**

In order to graph the inverse of a function, you must graph the function then exchange all x values with all y values. You can also check here on the third slide to see an example of a graph, or for any of the inverse information.

And that concludes my scribe post for today. To reiterate my earlier statement, tomorrow's scribe is:

**KADEEM**

### Today's Slides: February 26

To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

## Sunday, February 25, 2007

### I know the anticipation is making you anxious!

I know is looking forward to my horrible first scribe (not really), BUT your just going to have to wait one more dreadful day for it, ha ha. Okay that's all i wanted to say. Enjoy the rest your Sunday.

### A Transformations Video Lesson

I tried to collapse the better part of two classes into this 16 minute, 20 second video. After watching this you should be able to do almost all the questions in exercises #8 and #9.

Two things: For some reason the video is about 12 seconds ahead of the audio. Also, at one point I misspoke and described y=f(-x) as a reflection over the x-axis. That's not right, it's a reflection over the y-axis. Everything else I said about that transformation is correct.

Here's the Google video ...

A lot of the video quality was lost. There's a better (not best) version here. Click that link to see a much better quality video.

A nice thing about video ... you can [pause] [rewind] [repeat] as often as you like until you "get it." Nonetheless, feel free to ask questions ... in the comments to this post or when I see you on Monday.

You may also find these links helpful ...

All about vertical reflections

And you can find a tutorial and interactive java applet here to review and learn all about vertical and horizontal stretches, compressions and reflections.

Let me know which link you liked the best. ;-)

## Saturday, February 24, 2007

### Some helpful sites.

http://www.bmlc.ca/Principles%20of%20Math%2012%20%20-%20Transformations%20Lesson%204.pdf <-- This site contains steps for how to determine each parameter in a standard transformed function, such as stretch, shift, etc.

http://www.mathsnet.net/transform/index.html <-- Here's some interactive tools to show how all the parameters work.

http://archives.math.utk.edu/visual.calculus/0/functions.12/index.html <-- Good summary of the principles of translation.

I hope these sites can help, and I hope this kind of makes up for those classes we missed.

## Thursday, February 22, 2007

### Scribe's Scribbles

Finally, I get a chance to scribe. After being a victim of technology for the first couple of weeks and then having to deal with some postponed classes, I can finally write a half-descent scribe.

Well.. where should I begin? I guess the beginning of class would be a reasonable place. I walked into class only to see Mr. K. playing with his new favourite toy, actually I think he was just setting it up for the day's lesson, but we all know he loves to use it. Then, Mr. K. handed out part two of "The Test of Doom" (Chris). This consisted of two measly questions that represented the graphing portion of the unit test. However, once the test started those two questions seemed to get a little less 'measly' and a little more difficult (or at least it seemed that way, most people used the whole 15 minutes and were rushing at the end).

After those few minutes of tension, the room became its friendly self once again as Mr. K. pulled the Blog up on the Smart Board, and starting a discussion about BOBs (Blogging on Blogging; see the pc40sw07 Blog). The talk of BOBs went something like this:

1) BOBs are to be done BEFORE the test (preferably 2 days before)

2) The purpose of the BOB is to help us see how we've improved

and show some of the things we need to improve on.

3) Mr. K. needs us to post BOBs (preferably 2 days before) so that

he can help us in areas we have problems with before the test.

4) Finally, Mr. SiwWy posted a very good BOB because of the way

he reviewed each of the mnemonics we learned in this unit.

Following that, we entered our new unit, Transformations. Basically it has to do with Functions (not only Trig. Functions) and how they can be transformed. For example, if you are given the functions f(x)=sin(x) and g(x)=sin(x-2):

This also works for any other function. For example, if you are given the functions f(x)=(x)^2 and g(x)=(x-2)^2:

Now, both of these examples used a "phase shift" which adds to the x-coordinates. However, I could have used the sinusoidal axis or "vertical shift" which adds to the y-coordinates. Actually any of the parameters from the formula:

Then Mr. K. gave us a couple questions, but they were in the form of a COMPETITION. Once again we had people racing up to the front of the room with arms outstretched and shoulders rubbing together to write on the Smart Board. Both occasions ended up with each of the participants with a marker in their hand, so Mr. K. had to declare the winner almost by photo-finish (JoJo). However, there is no need to post these questions in my Scribe post because Mr. K. has a Smart Board!

"Go out and commit random acts of kindness!" -Mr. K.

Goodnight everyone, I'll see you tomorrow.

Oh, Almost Forgot, THE NEXT SCRIBE IS...

...KADEEM!!!

### Today's Slides: February 22

To see a larger image of the slides go here. When you get there you'll see a button in the bottom right-hand corner that says [full]. Click it and the slides will display in full screen mode.

## Wednesday, February 21, 2007

### BOB

Mathematics, the science of patterns, has been a challenge to all of us ever since we started school. From Addition to Subtraction, then Multipication and Division, we eventually end up in the midst of a very chaotic world filled with cotangents, quadratic formulas,

**circular functions**and things like that. As the adventure goes on we face the horrors of the Circular Functions Quiz but we still stand strong and now the real challenge of this unit comes closer...

**"The Test"**...

DABC.... I seem to always forget how to graph sin and cos functions... If only I had a way of figuring a way to remember it a lot easier... Hehehe... DABC really is a lot of help for all of us when we're graphing sine and cosine functions....

There's one thing I'm sure everyone will agree about......

One of the things that got me so confused was the

**for**

*exact values**cosecant, secant and*

*cotangent.*Apparently, we're suppose to get the functions reciprocal equivalent (iunno what to call it...):

cscÎ¸ = 1 / sin Î¸

secÎ¸ = 1 / cosÎ¸

cotÎ¸ = cosÎ¸ / sinÎ¸

Well that's it for this post folks... Hope you have yourself a great day.... And Good Luck on the Test...

**REMEMBER! KNOWLEDGE IS POWER!**

Can you be random-ER than this?

### BOBin' for apples?

Something that made me happy about this unit, circular functions, was that when math gets tough, make it simple. Let me explain, if you can count 1, 2, 3, and sometimes 4 then you can certainly learn about the unit circle. That was such a relief. heww. Sometimes I still can't over the fact that I get math (and sometimes I even enjoy it).

Something that I would like to do is study with people that I don't really know from class. I find that it's true, that when I study with people (in my math class) that I don't know, there's a less chance that I will get off topic and start talking about the 'latest news'.

To my precal 40s class, good luck to you all!

### The test of Doom

Morning Class:

In the morning , we were given, as told, the greatly anticipated circular functions test. It was not what I had expected, and to be honest, I expected a lot more from the test. But still, the morning class was an intense one, as an ambient tension spread across the class once the test was given out. Complete silence overtook the room, with the exception of pencil scratching and calculator button mashing. Class progressed with this seemingly ominous silence, only to be interrupted by the substitute teacher telling us to place our tests on the desk at the front on our way out of the class. Period two was imminent, so some scrambled to check over their test or just to finish their test, while others blissfully laid their papers on the desk of fortitude. Once the bell rang, everyone handed in their tests, if they did not already do so, and that concluded the morning class.

Afternoon Class:

There's nothing much to say concerning the afternoon class, as we really didn't do much. We were "assigned" to read pages 10 to 16 I believe, and to complete the assignment it stated on the board. When did we ever receive this assignment? It's odd because I could have sworn he said something about "applied 40S." I really didn't know what he was talking about, but class turned out okay. The afternoon was a big slack class, everyone just sat in their desks (or moved around) and completed homework and did practice problems and such. I myself finished homework in the class, and talked about the test from the morning class. Many of us were still conversing and arguing about questions that were on the test, and in many cases one side of the chattering parties ended up feeling regret for realizing their mistakes on the test. For the rest of the class, not much else happened except for the aforementioned activities, and we didn't learn anything, so I don't think I can say anymore.

Now I'm just wondering whether we're still going to have to complete the rest of the test, which is the graphing part of it. I was under the impression that this was going to be given to us in the afternoon, but it wasn't, so I'm assuming that it will be given to us tomorrow morning. Am I correct? Well either way, I think I, as the rest of you should, am going to practice some trigonometric graphing problems to prepare for tomorrow.

Good night everybody! Study for tomorrow's graphing portion of the circular functions test (at least I think it's still on for tomorrow) and I wish everyone good luck!

### blogging on blogging

## Tuesday, February 20, 2007

### BOB-A-THON

For the class so far I say that I'm doing alright. Minus the Homework blunders and the super secret surprise quizzes that are being put out. I'll say that Math for me is still on the bright side. Haha. Yet I still get confsed sometimes on the most basic question with concepts that I should of learned a long time ago. Ha Ha Ha.

Something cool in the class is of course the SMART BOARD. Ahh read the paragraph above if you don't really understand it.. It can really incorporate learning to a WHOLE NEW LEVEL. A moment of clarity... woo had to be ... DABC. Haha. It really helps on creating sin/cos graphs. It gives important options and makes graphing easier in more ways than 1. In the real world.. PIE is everywhere. Hahaha. MmmMmm cherry Pie. Hahaha Well anyways. Haha

Well Good luck on the test tomorrow everybody. Studying anyone??

### Blogging on blobbing

### BEE! OH! BEE!

My progress in the class has been okay, so far...could be better but it's all right for now. It's probably because of that surprise quiz that we got...kind of caught me off guard...I guess it caught everyone off guard...and it was one of the rare times that I froze and blanked out!!! It sucks because by the time I figured how to do the first question..time was up! I guess I just need to learn how to relax and not be so tense before a test/quiz.

Something that I learned that I thought was "cool" is the way the unit circle is set up. It's quite amusing...I was just in awe when we first learned how to decipher where the angles lie and what coordinates they had.

Something I didn't quite get before was graphing equations and figuring out how to write equations for graphs...it is still quite difficult for me but I understand how to do it..it's because I'm quite slow at it and I guess my brain doesn't work as fast as a lot of the other students in the class.

I have not yet encountered something we learned in class with the real world yet or in another class.

Radians and degrees are both similar in a few ways. For one thing, they are both used to give the magnitude of an angle. They can both be applied to the unit circle. Another thing is they can both be given in a positive or negative value. Although, there are similarities to both radians and degrees there are also some differences they both contain.

Radians can be written with pi whereas degrees are written with a degrees symbol. Radians are easier to work with in the unit circle, in my opinion because fractions are used whereas in degrees a multiple of some degree is continually added on. Another difference I found between radians and degrees is that I only know of radians being used for the unit circle whereas degrees can be used in temperature.

*Also, good luck to everyone on writing the test!*

### BOB

### BOB

Okay, so maybe our class isn't THAT dramatic and exciting but it's still very important to review and study our material. I for one have taken this course before (A WHOLE YEAR AGO! PHEW!) and even though I knew most of the things we were learning in this unit, I was still able to take away some new things I hadn't known before. Math is a science of patterns, and by using patterns I was able to memorize the unit circle and all the exact values associated with the trig functions within it. My past class failed to apply such an extremely effective strategy of learning towards the course.

So with that said, I'd like to wish everyone good luck on the test tomorrow, don't stay up too late studying and get a good breakfast. Trust me I'd much rather be completely focused on the test then worrying about filling your stomach cause it won't stop grumbling =D When it's all said and done, we'll be on this adventure together and with hard work we surely will finish this adventure together.

### BOB

### BOBMANIA

Hey everybody! This is my first ever post on this blog ever, or any blog for that matter, so I don't exactly know how to start. I guess I could start by saying how much I love this class so far, and then progress into what we learned in the class so far, which is the almighty unit circle.

Throughout our unit of the unit circle, I haven't quite encountered any insurmountable roadblocks in terms of difficulty comprehending anything. Overall I understood everything, except for those classes which I missed (for worthy reasons of course), but I did manage to catch up thanks to the oh so helpful podcast. Homework was another big thing, and I really am glad that for a change, I am fully completing it and am not procrastinating in doing so. I really hope the rest of you have been doing your homework too. I think it really helps with understanding each aspect of the concept further and helps with subtlizing each problem so that new problems of a similar nature won't present as much tribulation as it could have. And seeing as our test is coming up tomorrow, I think the homework Mr. K has given us can provide us with much practice solving problems that will probably be on the test. I think that I, as I advise the rest of the class to do, am going to utilize these questions to us as help to prepare for the gruesome fear-inducing test tomorrow.

But try not to forget all the mnemonics and tips Mr. K has given us to help us remember certain segments of the unit, such as:

- The exact values of the functions sin and cos found on the unit circle follow the pattern of 1, √2, √3 (all of which are over 2). Visualize where the angle is found on the unit circle, then use this to help imagine what the exact co-ordinates of that point are.
- The exact values of the tan function (sinx/cosx) follows a pattern of 1/√3 ,1, √3. It ascends along this pattern as it travels away from the x-axis, and reaches
**undefined**at the y-axis, then descends back down this pattern until it reaches the x-axis again. The same goes for underneath the x-axis, but remember that tan is negative in quadrants**2**and**4.** - F(x)=
**A**sin**B**(x-**C**)+**D**F(x)=**A**cos**B**(x-**C**)+**D**

Remember**DABC**to remember the order when graphing a trigonometric function.**D**->**A**- >**B**->**C**Start by visualizing or drawing in(using a dotted line) the**D****A**, subsequently determine**B**by using:

B= 2Î /Period

Use this value to scale the x-axis. Once all of those are done,**C**(the phase shift) will be used to show draw how much the graph is shifted horizontally**.** - Think proportionally! It's a great way to think and a logical method to solving problems, and is accurate and simple as well.

Well, sorry if I made this BOB too long, I just got carried away. =/ Well, I guess I'll end this off here by saying that I really like this class, and I'm glad I'm understanding everything perfectly so far (despite what the recent quiz might show). So, I wish everyone good luck on their test tomorrow, and don't forget to study!

### BOB

### BOB

as for how well i think I'm going to do on the test, we can just say I'm not very good when it comes to anything that goes by the names of: Test, Exam, or Quiz.

P.S.

Good luck to everyone... (spiritually)

### BOB

**, something like that. Haha. You get the point. He's right though. For example, the unit circle. If you can count 1, 2, 3 then you could memorize all the radians, the sine, cosine and tan. Also, Mr. K taught us "**

*"math has different kind of patterns"***for graphing the function. The whole working in group thing was a good idea. I would say it was pretty fun. A lot of people also said that they learned more through working in groups. I have to agree, I did learned a lot of and understood it better working in groups with the whole sharing ideas about how to solve the problem. That's all for now.**

*DABC"**GOOD LUCK ON THE TEST TOMORROW & STUDY HARD! :)*

Have a good night everybody.

This is JEEENG sining out.

### BOB

The class I found the most enriching, was the class in which we had the Pre-Test, because it showed how everyone put their taughts on paper, and what we did not know, the groups had cleared up. I found that class to be one of the most successful, because it showed how much teaching group work can bring. Good Luck on the test and Study Hard!

### BOB

**Smart Board**FTW!

### FUN CLASS!

... No I'm just kidding, I'm still scribe for tomorrow's class :P

## Monday, February 19, 2007

### BOB

### BOB - Circular Functions

As I said earlier, this class has been such a good experience, but there was one class in particular that stood out as both a fun and learning experience. When we wrote our pre-test for the unit, there seemed to be a sense of tension in the air while we wrote the test. Everyone was silence and the sounds of pencil scratching, calculator punching, and the blowing of eraser shavings off one's desk filled the air. I myself was not expecting such a "tricky" test so I was also thinking and working furiously. After Mr. K. told us to stop writing and split us into groups, the sounds of frantic problem-solving seemed to morph into a more relaxed sharing of ideas. I feel this class was great because different people got a chance to get together and share their ideas and methods, all of which were greatly appreciated. Finally as Mr. K. shared the correct answers with the class there seemed to be a great excitement as if each answer was the winner of and Oscar. Groups exploded with cheers, fist-pumps, and hi-fives to members of their groups whom they weren't friends with before. That is why I believe that this was the best class; it made the students of this class a bit closer and I'm pretty sure that no one here is afraid to share their ideas with someone they feel close to.

Finally, I wish to say a formal GOOD LUCK! to everyone for Wednesday morning's Unit Test. Remember Sisyphus, even if you believe it to be impossible, try your best...

### TIM BOB

I believe that I have a good understanding of the unit. I will admit that at times I was puzzled until I seen how it was done. I'm trying to think of a specific topic that I struggled with, but I can't seem to pull one out. Overall, each lesson included struggles for me; finding the right path that will lead you to the final answer. I have pulled through and out of the tangle often enough though and so I think I'll be fine.

What I found to be interesting was mainly the radian angle measurements. It was something completely new to me and made me think. Now understanding radians, I know what that "radian mode" in my calculator means =). Also, I like the fact that converting to radians and backwards, finding arc length and all of that stuff was quite interesting. They all have to do with proportions like Mr. K stated earlier and that's something that definitely helps me understand things (quite logical if you think about it).

Blogging Prompt:

Now, thinking about how I could relate radians and degrees, I can generally say that.. (thinking of the right words) they both can identify specific angles and the relationships between them, such as coterminal angles, number of rotations, related angles, and all that fun stuff.

Thinking about the differences, the first obvious difference would probably be the fact that radians usually consists of fractions and often have something to do with the value of "pi", whereas degrees are whole numbers + decimals and include the degree unit. They have different values that determine the same point?

Well those were off the top of my head.. I think I'll end this here.

**____This Pre-calculus40S class is awesome. I haven't worked with an intelligent group of people in my life that day by day challenge each other and ME. As a reflex, I have to keep up with the pace of learning that the course requires. The first unit is CIRCULAR FUNCTIONS. In my opinion, this unit can be so easy if you kow your 'thing'. Otherwise, it will be confusing and difficult to grasp. Indeed, converting radians to degrees and vice versa, finding the sector, arc length, etc. are easy. However, when it comes to graphing equations and deriving a SINE or COSINE equations from graphs, I can be perplexed. Currently, I am worrying with the fact that I can mess something up with silly and simple errors prior to solving equations or graphing functions. Today's class and the pre-test last week sort of set the blueprint of my own building of learning. Now, all I have to do is work my way to the top and to nail the answers for every single problem thrown at me. I will never forget the minor errors that our group made today when it appears on the test. Everyone learns from their mistakes. The dictionary helps me a lot too and so are the scribes that are posted every night. They help me refresh my memory about the day's lessons. Groups definitely help mind enrichment due to the fact that integration of minds exists and therefore enhances every member's knowledge about a particular topic. like today, my group members and I shared answers and opinons about our answers. It felt good! Though, I don't want to get to dependant on groups because most of the course will comprise of individual work like tests and quizzes. Our first test is on wednesday and no group member will save anyone's life there, will there? So, that's my perspective. Also, good luck on the test!**

### B.B.T.T. (blog before the test) or BOB

First I thought it was gonna be quite a struggle for me since I hadn't taken math for a year and that I forgot most of the things I've done last year. It was definitely a struggle for me the first few days because my brain was still in idle mode and I was trying to make my brain get back in rhythm. Fortunately, after a few days of doing math exercises, I was able to finally understand the unit. At first I didn't understand how to convert degrees to radians and vice versa, but after Mr. K gave us the first set of Math Dictionary notes, I finally understood it. The Unit Circle was not that hard to memorize after you work with it after a couple of exercises. Also another area where I was struggling is at graphing trigonometric equations and creating an equation from a graph. From the pre-test last Thursday I finally understood how to scale the graph and from today's class I was finally able to understand the concept of making an equation from a given graph. I'm still not very confident about it, but probably after a few review exercises I should be good.

So, good luck on the test on Wednesday guys and gals!