Tuesday, March 31, 2009

BOB, Show Some Identification Please :D

Since our test is on Wednesday I've decided to BOB already. I know what some of you may be thinking... "It's Spring Break! Have fun! It's to early for a BOB!" But you know what ? I have lots of work and I might as well get this over with. >__<

I understand this topic. I really do. My quiz may state otherwise but I UNDERSTAND. I swear! It's just that I don't have many clever ideas and that I tend to do things the long way. I guess this means I have to study.. lots. :(

Well I guess this is basically what we need to know for this unit:

1. Work with the complicated side of the identity first.

2. Rewrite both sides of the identity in the terms of sine and cosine.

3. Use a Pythagorean identity to make a substitution (sin^2x + cos^2x = 1, 1 + cot^2x = csc^2x, sec^2x + 1 = tan^2x ). So if you have 1 - sin^2x for example, substitute i
t with cos^2x.

4. Simplify complex fractions or rewrite fractions of sums and differences with the same common denominator.

5. Factor (especially use difference of squares).

Oh wait I lied... there is ONE rule: NEVER EVER CROSS THE GREAT WALL OF CHINA !!


Then there are sum and difference identities...

sin(a+b) = sinacosb + cosasinb
sin(a -b) = sinacosb - cosasinb
cos(a+b) = cosacosb - sinasinb
cos(a-b) = cosacosb + sinasinb

Use them :D

Just substitute the values of a and b. Then evaluate. You might have to find out what the angles are but you guys are all geniuses ;)

Oh and then there are those double identities. Look those over because we are most likely going to need them :)

I guess that's it... well that was short :D

I just noticed that I use smiley faces a lot. :O

Friday, March 27, 2009

Thursday, March 26, 2009

Wednesday, March 25, 2009

Scribe post for March 25..

Hi everyone,I'm Trinh and i'm the last one from the scribe list.
Anyway, I just go straight into what we've learned this morning because my network connection is not working really well. It could be disconnect anytime.

First, Mr.K put us into group and we started with some homework problems.
we apllied the sum and difference identity of so we can get the first line in the picture above. You could see that

and
Sub that number into the expression, we get the next line and we could find out the answer.


For the next question





We still using the sum and difference but this time is and , after you expressed, you'll see 2 opposite expressions, you could cancel it right away for short and there are left, that gives us .

The next question is more complicated than the first two,








then we started to prove how can we get the sum and the difference identities equation.




we've not finish this part yet and Mr.K said we're going to finish that tomorrow .

Another thing is about our mark, Mr.K will give a code for each of us so we can check out our mark online. He'll finish it on Friday or on the first day back to school after spring break. We have to go see him to get the code.

Tomorrow is PJ/Crazy Hair Day - The Chris Frolic Comedy Hypnosis Show ($2/ticket)
So make sure you have the ticket for the show tomorrow.


Today's Slides: March 25

Here they are ...



Monday, March 23, 2009

First scribe of the yr

This is my first scribe for this class^_^
I miss the first 10 min of the class, but I think we didn't do much before I come in.
We start off with the question: to prove the identities
This one is simple that just use the formula: to replace then simplify it. there fore it's QED.

For the second question we got 2 solutions which both of them are all correct, bit one is less work than the other one.



VS.
They both are right but I would do the second one.
In the first solution he turned everything in terms of cos and sin, which we will do for most of the questions.
In the second solution, he recognize that so it made the work much more easy and faster. This might not work for every question, but it will work for some of them.

For this question she used the difference of square. Which in Mr.K's work "cleaver idea", he said that in every identities that must be some cleaver idea will help u to proof the identity.

Of course the most fun& important part of class today the dance


I kinda forgot the dance could any one help me and leave a comment to put the dance that we did.


then we did these questions to end the class of today.
In this kind of problem u just have to understand the formula to able to solve the problem.
Hope that everyone understand me. ^_^
Oh next scribe is.........trinhn92 ^_^
Homework for the day is ex16 all 1st 19 question and any 5 out of the last 10 question.

Spirit Week Themes
  1. Monday: Sports Day - Sports Obstacle Course
  2. Tuesday: Superhero Day - Save the Day Relay Race (you could dress up in a costume or wear a t-shirt that has a superhero logo on it)
  3. Wednesday: Twin Day - Talent Show
  4. Thursday: PJ/Crazy Hair Day - The Chris Frolic Comedy Hypnosis Show ($2/ticket)
  5. Friday: Colour Code Day - Grade War Gym Riot (gr.12s wear green; gr.11s wear blue)





Today's Slides: March 23

Here they are ...



Friday, March 20, 2009

Eliminate Discrimination

Today we celebrated the International Day For The Elimination of Racial Discrimination. We discussed many things around the ideas shared in these two videos. (I LOVE) Dr. Suess. ;-)_

The Sneetches Part 1 of 2




The Sneetches Part 2 of 2




And here's something else for you to think about ...




Feel free to share your thoughts in the comments to this post or write your own discussion and label it "On My Mind".

Thursday, March 19, 2009

Yay Identities!!!!!

Hey everyone

Well to start off class today, Mr.K wanted to talk about the "Blogger Hall Of FAME!!". We took a few votes on the subject and here's what we decided:

1) It takes a MINIMUM of 12 votes to get your blog into the blogger hall of fame.

2) NO anonymous votes.

3) NO voting for yourself.

Once we were done with our little bit of classroom democracy, we split up into groups to work on some practice problems. Once we were in our groups, we did a little recap on Pythagorean identities. Remember:

eq=sin^2\theta +cos^2\theta =1

As practice, we simplified a few simple expressions using Pythagorean identities when we could.

Example #1

eq=csc^2 t - cot^2 t

1) first change the expression to only use sine, cosine, or 1

eq=\frac{1}{sin^2 t } - \frac{cos^2 t }{sin^2 t }

2) this leaves you with two fractions with the same denominator. Rewrite the expression

eq=\frac{1- cos^2 t }{sin^2 t }

3) since the numerator is a pythagorean identity, we now know that the numerator is equal to sin^2 t

eq=\frac{sin^2 t  }{sin^2 t }

4) the numerator and denominator can be factored and the answer that is left over is 1

Once we had finished simplifying the expressions, we found that two of the expressions simplified to the same thing, in this case 1. We used them to write the equation


To check if this is true there are a few strategies that we could use. These are:

1) Work with the more complicated side of the identity first

2) Rewrite both sides using sine and cosine

3) Use a Pythagorean identity

4) Simplify complex fractions or rewrite them

5) Use factoring (especially to create differences of squares)

A very important thing to remember when proving trigonometric identities is that you have to drop down "The Great Wall of China" and you can NOT cross it. This is because, when proving an equation, there is no way of knowing whether or not it is true.

So now that we have covered proving trigonometric identities, on to a new subject!!

EVEN AND ODD IDENTITIES!!

sin(-x)=-sinx cos(-x)=cos(x) tan(-x)=tan(x)

the sine and tangent functions and ODD functions

cosine is an EVEN function

ok so now i've gone through pretty much the entire class of today. There is only one more thing from class that i must remind you of:
YOUR DANCING TOMMOROW!!!!
so i'd bring something comfy to wear. Mr.K said that as soon as you get into the room get into groups of four, with at least one person in your group that you have NEVER worked with.

One last thing. The scribe for tommorow is..... YI NAN!!!! =D


Today's Slides: March 19

Here they are ...



Wednesday, March 18, 2009

Trigonometric Identities......BEGIN!!!

Hey guys! It's me, jayp (AKA PJ)! Today we started what seems to be a very exciting unit in our Pre-Cal Class and we also got a little side lesson on the Greek Alphabet!

So starting with the main part of this scribe post, the NEW UNIT! It gives me great honor to be able to introduce to you all, TRIGONOMETRIC IDENTITIES!!!!!
Okay so just in case you didn't get the picture today in class, or you don't get it right now, this picture explains what Trigonometric Identities is all about! So the girl in the picture has many different hairstyles on so she has many different looks or identities, but they are all the same person!


What was shortly explained above is pretty much what this unit is all about! In this unit, we look at the different identities or "looks" trigonometric functions have. This means we aren't exactly solving equations. We are manipulating expressions. As Mr.K put it, we are "algebraically massaging" expressions.


Have I lost you? No worries. Here's what I mean.


In class, we looked at the number 3. How many ways can you write the number three?

Well there's 3.0,
,, and so on. These all look different, but they all mean the same thing. They all mean "3".


Now, because the unit is called "Trigonometric Identities", we will be dealing mainly with the trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent). Rather than just plain old numbers, like "3" (Sorry "3").


In class we first talked about how all of the trigonometric functions are made up of two main functions: sine and cosine.

This means,










Now that we had that in mind, we went on to answer some questions from the Smart Board. All of the questions asked us to take an expression which contained multiple trigonometric functions and rewrite them using only the sine and cosine functions and the number "1".
Before you start asking questions about this, yes I made these videos and yes that's me writing things down.

video

Here is a YouTube version if you find this too small!

After these questions, we looked at the Pythagorean Identities! Now this is a little complicated for me to explain here in words (mostly because my head is POUNDING at the moment) so I decided to make a little video!

video
YouTube Version

For some reason the end got cut off. It supposed to say "It can be further reduced to 1."

Now if you didn't get that, feel free to leave me a comment and I, or one of my fellow classmates will be more than happy to answer your question!



Earlier, I talked about how the Trigonometric Identities unit is all about manipulation. It is also about proving things. I'm in a video-making mood so I made a video for this too!

video
YouTube Version

Gotta remember that "Great Wall"!
NOTE: Because you can't put equal signs on the "Great Wall" you cannot solve this as if it were an equation. You must manipulate one side using what you know about identities in order to solve it. (Thanks Anthony for catching that!)
BTW, Q.E.D. stands for Quod Erat Demonstratum which means "
which was to be demonstrated".
Read more here.


We're almost at the end of today! Next we talked about how we could get other identities from what we have just learned! Cue the VI
DEO!!!!

video
YouTube Version
LOL! The music ends early. Darn Movie Maker and laggy computers!!! xD


Tada! This is basically everything we have learned today about Trigonometric Identities! Oh right, about that little mini lesson on the Greek Alphabet. During this unit, many Greek letters will show up. Don't be alarmed with how they look, treat them just like "x" or "theta".

Any who, I was going to make a video about Greek Letters as well but it's getting really late. If you are really interested, wikipedia it or look on the sidebar in the "Equation Maker" thing. The Greek Letters are found under "Characters" and if you hover over them, it tells you their names!



LOL! So I hope you enjoyed my little scribe post with all of the videos. Leave me a comment if they don't work and I promise I will fix them right away!

And now I have the honor of announcing the next scribe! The next scribe is Jessi? Yay Jessi!

P.S. Thanks to jamendo.com for the music! All the music there has a creative commons license so you can use it for free! And the music there is actually pretty good.

Today's Slides: March 18

Here they are ...



Tuesday, March 17, 2009

BOB

I had a lot of trouble with this unit, mainly with reciprocals and those long questions. I couldn't remember most of the steps a lot of the time. Though, I've been going to the library with a friend and my laptop to study (I downloaded the entire unit. =p) And as a result, coupled with the lessons in class that I kept flashing back to, I think I can do it now. The pretest especially helped me with this, because I actually did a large chunk of that uber question the right way!(Score)

I'd have to say that this unit with the exception of Reciprocals and gigantically long questions, was easier then the last.

Thanks for your time.

-ConstantEcho

BOB from the dead

Very sorry from the really late post I wasn't allowed to go on the computer Sunday and Yesterday because I was sick. It gave me time to study on the topics that I was bad at like the Modeling and Reciprocal Functions. Too bad I wasn't able to review stuff from the blog until today.... But I have my handy notes anyways.

That's it and good luck everyone! :)

Monday, March 16, 2009

BOB the Second

Okay, time to make another reflection on my thoughts about the unit. First of all, the transformations unit started off easy for me.. then came the topics like the reciprocal of the graph and the word problems where I really had a hard time dealing with. I guess it just takes practice to get used to how things work with those.

The pre-test that we did today gave me a heads-up on what to expect tomorrow and it made my mind clear on stuff that I didn't really understand.

That's it for now. Good luck on the test tomorrow, everyone! :)

PokeBOB! Gotta... blog em all? Idk..

Haha hey Precal 12 peeps ! Matthew Aka Pokemon Champion here with my little BOB for you all. The pretest today really helped me get all my thoughts together about this crazy math stuff XD Also sorry group uno of today for convincing you that the wrong answer was the right one haha If it makes you guys feel any better I get it now =D

Anyways... things to remember!

Parameters A B C and D and what they do...

A f [B(x-C)] + D

A- Vertical Stretch/ Compression
B- Horizontal Stretch/Compression
C- Horizontal Translation
D- Vertical Translation

Another thing to remember is how to determine what functions are even, which are odd and which are neither.

IF f(x) = f(-x), then u are dealing with one very even equation.

IF f(-x) = -f(x), then you have an odd equation.

IF neither of these apply then your equation is neither even or odd... Maybe its not even an equation at all O.o OoOoOo.. just kidding haha

But yeah as long as you've been keeping up to date on your hw and are studying hard... this test should be a breeze! =D

I think I'm going to go to sleep now because... I am super tired XD So good luck on the test 2morrow and goodnight everyone! ~Matthew

Kale's Bob

Hey there folks, it's your boy Kale here. Just gonna reflect on our most recent unit, Transformations. This unit was very good for me, because it's just a bunch of algebra and graphing, the good ole math that I love doing. We started off with reviewing some sine and cosine waves, and got into parameter A, B, C and D and how they shift and stretch our graph. We dug deep into the world of asymptotes and such. We concluded this grand unit with some real life problems, which definitely got me into math a lot more than I already am.

Good luck to all, and to all a good night!

Happy St. Patrick's day tomorrow, everyone wear green!

Jonno's BOB

After doing the pre-test, i think i'm just about ready for the real test. I found this unit relatively easy. However, there were some parts that i don't have total confidence in. This unit i learned:
-how to do sin/cos graphs and all those word problems relating to the graphs
-reciprocal functions graphing
-even and odd functions
-finding the inverse function of a function
-transformation or graphs

I think that pretty much sums up what we did this unit...

The part i'm not so confident in, however, is graphing absolute values because i wasn't there that day. But still, i think i know enough of it to get through the test.

I'd like to say thank you to the people who helped me understand reciprocal functions a while back and good luck to everyone on the test tomorrow.

BOB

I found this unit a bit more challenging, but I like how the last unit has a nice transition into this one. The one thing I had the most trouble with is the reciprocal function. That type of transformation is a bit harder to grasp, however I think I've got it down now.

As for the pretest, I found it extremely helpful, it clarified many of the questions I had. I really liked doing the pretest the way we did it. I would recommend studying it for the test tomorrow, all the concepts we need to know are in there.

What we should know....

Well we should know how to do basic transformations, stretches before translations etc.
We should know reciprocal, inverse functions and how to derive g(x) from f(x) and f(x) from g(x).
Know the flips over the x and y axis.
Don't get mixed up with inverse and reciprocal functions. The reciprocal function is the one where the function gets put under one. The inverse is when f is to the negative one, this doesn't mean the function is to negative one though.

Good Luck to everyone, Luck of the Irish actually, tomorrow is St. Patrick's Day :)






Today's Slides: March 16

Here they are ...



BOB ..

Super late B.O.B.

Yes, im bobing the day before the test, shame on me.
Anyway, at first, this unit was pretty easy, but as soon as we started putting everything into word problems, things went downhill for me. During the pre-test earlier, that was the area which I found the most challenging.

I think I will do well on the test, as long as I study and do some practice questions on the areas that I need help in. There are still some things that I have to work on, like graphing reciprocal functions, but my main focus would be on the word problems.

So yeah, i guess i have a lot of studying to do.
Good luck!



p.s. Im going to add on to this when I get home.. hah .



EDIT:

yeah, so much for adding on to this. i fail at this blogging thing. My computer is broken (sadface) .

bob

Second Bob of the year.
I'm always confused by the Inverse Functions and Reciprocal Functions. Both of them share the same sign which is really hard to tell which is which.

The last part will be the part that I'm also confused at. You have to know the formula
g(x)=AsinB(x-C)+D Which I can;t really remember. And i still think i have trouble with this part.

I think I'm good with other parts
bye!!!


Scribe post

Hi, this'll be my attempt at a Scribe post, but keep in mind that I'm not very good at explaining things. Ahem..

We started off eating pie.

Yum.

Then we learned a little bit about finding the reciprocal of cos(x).
Our focus will be to graph 1/cos(x) or also known as sec(x).
First we begin with drawing the graph of cos(x).

Look for the invariant point(s) and draw the vertical asymptotes.
The invariant points are the points on the graph that aren't effected by the transformation. (So, at f(x) = 1 or f(x) = -1)

From this, we use the Dr.Sues method. Because it's the reciprocal, the x and y coordinates begin to bigger and smaller in the opposites of where they were going. So, they move closer and closer to their respective asymptotes... But they will never cross them. (Because asymptotes can never touch the graph lines.. Shed a tear for them.)

And there you have it! A (not so) beautiful graph of f(x) = 1/cos(x) or... f(x) = sec(x)!

This is all we did on friday.

I'm pretty sure I understand this correctly, but I'm not so sure if I've expressed that clearly enough so that others would understand it as well, so please feel free to comment and tell me how wrong I am! =D

-ConstantEcho