Saturday, February 28, 2009

022609 QUIZ DAY

Hello ladies and gentlemen, how are you? I'm Jennifer, I'm scribing for Thursdays class February 26th I believe. Well on 26th we had a QUIZ on translations and corrected it in class. The quiz was posted up along with the answers by the teacher. THE END . . . . just kidding

Well I think I should go over the answers and how we got that but since my classmates are so smart. I don't think it's necessary and considering the fact that the quiz was so straight forward. But since there seemed to have been some confusion near the end of class I will try to clarify things. Since it was the quiz that confused some people, I will not reference to the quiz. Hopefully you will be able to understand after my explanations.

Stretches/ Compressions
Vertical stretches/ compressions: A vertical stretch/ compression is represented by the form of
y= af(x)
Where a is the vertical stretch factor.
Example one: Stretch x^2 by a factor of 3.

All the y-values are now higher. We just stretched the graph vertically up.

Horizontal Stretches/ Compressions: A horizontal stretch is represented by the form of
y= f(bx)
Where the reciprocal of b (1/b) is the stretch factor.
Example two: Apply f(2x)^2 to x^2
The graph has just been compressed horizontally.

Vertical Shift; A vertical shift is represented by the form of

y= f(x) + d

Where d is the upward or down shift.

Example three: Shift x^2 up by 1 unit.

Horizontal Shift; A horizontal shift is represented by the form of

y= f(x - c)

Where c is the left or right shift.

Example four. Shift x^2 right 1 unit

NOTE: Watch the signs of your c, it is opposite.

All Together Now
af(bx - c) + d
Example five: Describe how the graph of y= -3f(x -4) +2 compares to y=f(x).
-3: reflects on the x-axis and stretched vertically by 3
4: moves f(x) right 4 units
+2: moves f(x) up by 2 units

Well that was basically what the quiz was on, translations. And as you can see near the middle of the post I came across some format problems that I just can't seem to fix ): I hope this will help you understand the mistakes that you might have made on the quiz. And if you still want me to go over the quiz I will if needed.

This took longer than I expected. I was even going to post what I have right now I was just gonna say we had a quiz, the end. But it didn't seem fair to my classmates so I did this. We do scribe on quiz days right? It was only tests that we can't scribe for.
Goodnight classmates.

The next scribe is shumei
Toddles see you all Monday!
P.S(I wonder what that stands for?) MR.K come back soon your class needs you!

Thursday, February 26, 2009

Wednesday, February 25, 2009

Reflecting on Translations and Transformations

Good evening everybody! It's WonderfullyExcellent, aka Alex. I'd like to start off today's post by saying HAPPY BIRTHDAY JOHN!
Hope you have a good one.

Now, to today's class. We started off right away with translations and transformations. We went through today's slides which were quite helpful and informative. Unfortunately the Internet was down and we could not access Fooplot, but if you were confused about anything try putting it on Fooplot yourself. Another unfortunate occurrence, I can't seem to be able to capture the image of the slides from today, so you'll have to view them yourself too.

What we learned today was pretty much a review of what we already know. Here's a review though:

When f(x)= (x) + 1 then the graph is moved up 1 unit.
When f(x)= (x) - 1 then the graph is moved down 1 unit.

The shift, whether up or down, becomes the new sinusoidal axis.

When f(x)= (x+4) then the graph is moved left, yes left, 4 units.
When f(x)= (x-4) then the graph is moved right, yes right, 4 units.

When f(x)= 2(x) then the graphs amplitude (the distance from the sinusoidal axis) becomes 2 above and below the sinusoidal axis.
When f(x)= -2(x) then the graphs amplitude IS STILL 2, the graph is just reflected (flipped over the sinusoidal axis).


Finally, when f(x)= (2x) then the period is changed. To find the period you take the number you have in front of x, in this case 2, and put it under 2pi. This gives you the period.

Remember, when the number in front of x is a whole number, the frequency between 0 and 2pi is increasing. When the number in front of x is a fraction, the frequency is decreasing.


Now, if you have the function f(x)= (4 - x^2)
and you change it to 2f(x)= (4 - x^2) then you are shifting the amplitude up/down 2 units. Basically you are stretching the graph vertically. Note; this does not affect the horizontal values.

If you change the same function to f(2x)= (4 - x^2) the graph is compressed horizontally 2 units. And if that two was 1/2 then the graph would be stretched horizontally 2 units. Note; this does not affect the vertical values.

After going through the slides, we corrected a portion of our tests, hope everyone did as well as they wanted too. If you have any questions or concerns about the test, post them on the blog or talk to either Mr.K or Dr.E.

Hope everyone found this post helpful, see you all in class tomorrow. Oh! Remember there is a quiz on all this stuff tomorrow, Good Luck.

The next person to have the privilege to scribe for tomorrows class is Jennifer.

Slides February 25th

Internet is back, yay! Here they are:

Slides February 24th

Here they are. Sorry for the delay.

Tuesday, February 24, 2009


Hello everybody! its me again jeck. I'm here to scribe for today. First of all, I'm sorry for being unfair to others. That was my first time to join a blog so I don't have enough knowledge about scribing or posting in blogs. Now this is my second time, please be nice if it is still awful! :p

Anyway, lets go back to business. Today we talk about TRANSLATION. At this time Dr. Eviatar can't post the slides that we talk about in class because there is some connection problems she encounter so I consult last years pre-cal class (winter 2007). Today's topic is very confusing for me like of the g(x) and f(x) thing.

Here's some slides from last years class:

We can locate the vertical shifts and horizontal shifts by this formula:

y=AsinB(x-C)+D or y=AcosB(x-C)+D

where C is for horizontal shifts which add to the x-coordinates and D for vertical shifts which add to y-coordinates. In general we can use this formula:


Here's some example:

y=f(x) + 1 => this function being moved up 1 unit. If the original point is (1,0) and moved up 1 unit, so the new point is (1,1).

y= f(x-5) => shows this function being shifted to 5 units to the right. if the original point is (1,0) then the point must be (6,0) because it moved to the right by 5 units.

I hope everyone can see the image and can understand me as well. I hope it help you with my little knowledge about translation. If theres any error or mistake just tell me and I will make changes as soon as possible. Have a nice day and have fun :)

The next scribe is WonderfullyExcelent

Friday, February 20, 2009

scribe for circular functions test

Hi!, im jeck and I'm here to scribe for today. Well, we had a test today and I had a hard time in answering those questions. I have nothing to say because we dont discuss anything today.

I hope everybody will pass the test today. If you dont feel you will pass the test then start PRAYING now, just like I did. :)

Best wishes too for Mr. K's wife surgery! (thanks Laika for reminding us about it)


I found this unit difficult. This is because I hadn't done math since grade 11, which was 2 years ago. Lots of the things we did, required formulas that I had to look up and relearn. (For example, the formula for area.) I've managed to figure most of those things out again, but I'll probably still need to do more work.

I did learn the things at the beginning of the unit (Converting degrees to radians, ect.) and I did remember most of the Trig things (SOHCAHTOA), so I am able to do this. =D

I guess that's my reflection on the unit.



I also apologize for being so late too. After going home from school I fell asleep.
MARY.L> pacifico, this is the escape program in that temporal dimension that the time-variant of john ly created
This unit wasn't a walk in the park, really. When Mr. Kuropatwa first introduced us to radians, I was like, "Huh?" As the days passed by though, I learned.
MARY.L> this acts like a TPDD, time plane dimension destroyer, that I use to travel through time
In every unit, there's always a hard part and an easy part. The topic that I found hard was the last one, the graph transformations —I think because it was rushed? Clearly I don't know. The Pre-Test enlightened me on that topic. I say thanks to Laika, Ingrid and Dr. Eviatar.
MARY.L> the ill intentions of the time-variant of john ly will be the punished by the Data Integrated Sentient Entity "Canopy Domain"
The topic that I found easy was the Manipulating Proportions. Expanding on why I think the topic was easy seems irrelevant, so I'll end my reflection in the next sentence or two.
MARY.L> choosing yes will transfer your universal unit code aegis to the world where codename: SNOW WHITE is a god
Good luck everyone! Look over your notes before the exam starts!
MARY.L> no will trap you in this normal world forever
MARY.L> yes?/no?

BOB in the morning

Sorry about doing this so late (technically early), but I had work yesterday.

So, the first thing we learn was about the 3 units of measurement: gradients (400 units), degrees (360) and radians (2pi). then we learn how to convert degrees to radians and vice-versa. Then we learn how radians are found on a unit circle, and we figured out the sin, cosine and tangent values for the angles. Then we learned the magical functions known as co secant, secant and cotangent. Then we learned the "k" or whatever letter you want to use, which basically is a variable and depending on what you say (e.g k is a element of integers) it changes. We used this to make a formula which would show us if the circle could go on forever how could you find the point when it went around the circle a certain amount of times.

Recently, we've been learning sinusoidal waves, which are curvy graphs. the formula for the graph is y(x)= AsinB(x-C) + D which determines how your graph looks.

Well i think i wrote most of it, I think I get most of the things on the test, but i guess we'll see today. Good luck to the rest of you (doubt you'll see this though, at least before the test).

B to the O to the B to the... NOW! XD

Super late reflection but I'm pretty sure that "Did you blog" mark will come in handy XD

Well, at first in this unit i went to check myanswers from the exercises and found myself asking "why is pi=180 degrees??" among other questions. All of my questions were however answered immediately in class in more detail than I ever probably needed.

Big things (especially for me to remember):

All the proportions of a unit circle... R/Pi = D/180= Total Area/Sector Area = blah blah blah

Other small equations like s=(theta)(r)


Determining ALL possible angles of a given sin, cos, tan, csc, sec, or cot value and hopefully being able to determine all the values of the common angles for those... (1/0 = undefined.... good stuff...). Also making sure to factor questions properly will help when it comes to the questions solving for xER... (yeah i know that E and "is an element of" are not the same and its supposed to be more curvy-like... but cereally.. just yeah XD)

Our latest addition, y(x)= AsinB(x-C) + D, and how all of these lovely parameters transform our lovely sin wave graph.... amplitudes... periods... i thought I was done with those terms once physics was done... oh well XD

And yeah that's it... one last GOOD LUCK! to all of us writing the test tomorrow... or... today by now... Just try not to hate me TOO much when I do awesome :p just keeeeeding! XD Good night to you all! Pre-cal 40S FTW! Peace~

Thursday, February 19, 2009

BOB - Circular Functions

Hey guises, I know this is late, but better late than never right!?
Well, let me start of this BOB thing by stating that thanks to PJ, I now know what "BOB" means...
"Blogging on Blogging!" Haha, I was so enlightened when I learned that :]

Anyway, I really don't have much to say without being redundant. However I still do have some advice for you!
- First off, remember that cos is relative to the x-axis and that sin is relative to the y-axis.
- Also, never write "sin" or "cos" without theta because well... That's just wrong! :]
- Don't forget that when given a negative value in terms of radians or degrees, it means that the direction is opposite that of the direction we would normally go. (Did that make sense? lol sorry)
- Remember 2kpi where k is an integer!
- Come prepared, with back-up ;D That is, pencils, erasers, lead, (graphing) calculators, rulers?
- Don't panic! Relax and read through the entire test before freaking out over a question that may actually be a breeze once you calm down, it's just a test!
- Oh yeah, don't forget to write one of these BOBs! ;D
- Also, look through the rest of the BOBs for more advice and tips :]

Alright, now a little solemn reflection... Just kidding :]
When we were first introduced to this unit, I was freaking out, lost, confused, and overall frustrated because the concept was so unfamiliar, plus I hadn't done any serious pre-cal math in over a year! The concept of dealing with relationships and proportions rather than formulas irked me a bit because I'll admit, my brain works like a computer sometimes. I dealt much better with plugging in variables into formulas. But, after getting the hang of it, I realized how much easier thinking in "proportions" was, and that it also provides me with better understanding!
At the moment, I can't really tell how I feel about the test tomorrow, I just hope I do well, really. Winging the pre-test and getting them all correct gave me a boost of confidence but I know I still need to review/study! Speaking of which, I should get to that now lol.

Good luck everyone! :D


I had a rough time at the start of the unit. Trying to remember how to get the radian equivalent of an angle had been a challenge to me but practice really helped me big time. I just hope not to disappoint myself tomorrow :)

I enjoyed this first unit. I guess it's all props to Mr. Kuropatwa as well for teaching us in very interesting ways.

I guess that's it for now.
Good luck to all of us!

And oh, remember to eat breakfast before going to school! Well, at least I will because I always eat breakfast in class..

KOB, kalebob

Hey there fellow bloggers, it's your pal kale here wanting to openly reflect on out unit "Circular Functions."
Here's my opinion:
This unit was a breeze at first, everything was going swimmingly until that dreaded sin wave! Every hope I had built up came crashing down, but with that lil' practice quiz today I must say I am pretty confident in a semi-decent test mark :)

Some things to remember:
sin corresponds with Y values
cos corresponds with X values
tan values equal sin/cos or Y/X
A unit circle has a 2π circumference

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


I've had some people asking for the pretest for those who weren't here today for the pretest, this is what you missed out on...
prepare yourself for bad quality pictures!

the answers are on the slides! but if you're able to make out the chicken scratch that i call "writing", then whoaa.. XD

and am i allowed to randomly post a blog like this? Mr. K? LOL

Jonno's Reflection on Circular Functions

So during class, i thought the stuff we learned was pretty easy. However, there were a couple of hard questions on the exercises. What really got me though, was questions 4 and 5 of the pre-test that we had today. I think i got it now though. I don't think there were any sections that were too troubling for me to understand. Best of luck to everyone in the test tomorrow.




Hey this is Rebecca and this is my reflection for this unit.

I found it pretty confusing when we began this unit, I didn't really understand the radians to degrees thing. After a few days and some help from my friends the light bulb went off! I also have had some troubles with the sin graph, that might be because I missed the class where we learned about it.

I found the unit circle pretty easy because we learned about it last year. I kept my pie plate from last year and that helped to refresh my memory!! Well that's all I have to say about this unit, hopefully the test wont be too hard. Good luck everyone!

I'll BOB you ! :)

To tell you the truth I felt that I had everything down pact. Now I don't feel as confident. XD

I understand the values in the unit circle. Radians and degrees seem interchangable, and I remember my quadrants and my cos and sin and everything else!

Looking for the unknown values of theta? I'm good. Seeing if a point is on the unit circle. I'm fine. Just being pi. Sure. I like pi :)

BUT I don't understand anything with graphs, or this ABCD stuff. I looked at the slides,I looked at the blog, but I think I need someone to explain it to me before I go crazy. Today I sort of got it but I'm not sure if I'll be able to apply this bit of meagre knowledge to questions on the test tomorrow.

My goal is 100% + I'm scared I won't achieve it =(

But I'm going to wish everyone good luck! And break a pencil ! (x

last scribe for circular functions?

Hi! It's me again but please let me introduce myself formally this time. I'm Laika and I'm here to scribe for the day. Since today is Thursday, this means our unit test on Circular Functions is tomorrow. In preparation for the test, today our class worked on a pre-test where Dr. Eviatar (cool name!) gave us about 25 minutes to tackle the questions on our own.

Quite a handful of the class was missing today which meant they’ve yet to meet our substitute teacher, Dr. Eviatar, for the week to follow. There’ll be plenty of time to get yourselves familiar with her so from the whole class, we warmly welcome you in our classroom! :D

Back to the main topic of this scribe, after the 25 minutes of self-work, Dr. Eviatar allowed us to form groups consisting only of 4 people maximum. We put our brains together and figured out the right solutions for the questions on the pre-test. Working with a group helped me out a lot since I didn't really know what I had to do for the last question. (Thanks Ingrid! Hahaha.) Dr. Eviatar took in a copy of the pre-test from each of the groups and for the remainder of the class, went over the answers with the help of the smartboard. Here they are along with the questions:

I hope everyone can see the images clearly. If not, I shall go make changes... tomorrow. XD Good luck to everyone on the test and best wishes to Mr. K's wife's surgery! :)

The next scribe is... jeck!

021909 Circular Functions Reflection

Hey guys,
Let me start offf by saying I detest circles and radians. Well the circular funtions unit isn't as difficult as it seems. I'm hoping I'll do well. Mr.K does a great job teaching, teaching us the; hows and whys. Not just stating the numbers and formulas that are hard to remember, like other teachers do.

Things we should know;
-converting radians to degrees, degrees to radians
- Arc length questions, portportions
- finding standard postion and finding reference angles
- solve for theta given different ranges
- exact values
- stretchs/ compressions, vertical/ horizonal shifts in functions
- unit circle
and so on.

and I don't get todays slides there's no questions or anything. So if you have the time care to tell me what we did in class today. But from my very little understanding it looks like what we did tuesday, is that right?

Well study hard precal classmates and good luck on the test tomorrow.


First bob for this blog!! Two bob today!!!
I think I know most of the stuff.
Still couldn't remember the unit circle.
I'm having trouble with the last part, because i forget to bring glasses that day*_*
I think I'm good with other parts.
I just have to study and review last part.
Good luck everyone + myself ^_^

oh bob~

hey guys! yeh its me again. don't worry, i'll keep this one blunt and short.

Recapping on your last unit, circular functions..
What i really liked about this unit, was how we were able to see the different methods of answering one question. Along with that, a little background info on how that method was discovered was interesting as well.
What i found hard about circular functions was and is the translations. The whole amplitude, period, and what-not got to me. maybe this is a side effect from physics? Ohh and the review questions from each exercise. i had allot of trouble recalling what i learned in grade 11... haha nonetheless, at least i know what i'll be studying tonight. What was easy for me, was most likely converting degrees to radians and vice versa. XD

Tips? i honestly don't know. i suggest you go over the slides, and redo the questions from the exercises that confused you the most.

okay im off to study, and i hope guyd are too!
byebye (:

Test time draws close!

Time to look back on what I've learned this unit! Flash back! Cue little floating thought bubble!

First in this unit we went over the unit circle. I learned about this last year in math and it was a great reminder! I forgot most of it but once we started again  it all came back. Sin of 30, 45, 60 degrees are 1/2, route 2/2 and route 3/2 respectively and opposite is true for Cos. The same holds true all around the unit circle. Sin is the y axis and cos is the measurement of the x axis. Tan is equal to sin/cos and is undefined at 90 and 270 degrees because cos is equal to 0 and you cannot divide by zero (except Chuck Norris).

If i remember correctly, we then learned about radians which was totally new to me. It was very interesting! 2pi is the full circumference of the circle and pi is half the circumference or 180 degrees. And I'm rambling on a lot.. I'll cut it short.

Sinusoidal axis, DABC, movement of graphs, up, down, stretching, amplitude, wavelength and finally period. :D Well I'm tired so I will follow up on one of those rules which someone said earlier get a good night sleep. 

:O *edited out for content* I'm not here tomorrow... umm Mr. K did you get an email from Ms. Troung... and your not here this week so probably not.... so ya...... see you all Monday..... I'll do the test then, alright Mr. K? :)

Slides February 19th

Here they are ....

Reflection on Circular Functions

Hey, it's your scribe for today! Except I'm just here to post up my reflection before the test tomorrow. Anyway, this unit was troubling in the very beginning but once I got the hang of it, it became tolerable. I'm not saying I'm a pro at circles though. :P

Among other things, the conversion from angles to radians was the part that frustrated me the most. Yeah, I know it's a pretty simple task and I've been practising it in time for the unit test. Grade 11 Pre-cal tipped me off quite a bit but after some review questions from the exercises, my memory is getting better.

Good luck to everyone on the test tomorrow! But luck's only a small part of it so remember to study, study, study!

Wednesday, February 18, 2009

Circular Functions Reflection

Hey everybody. Since I know that if I leave this til later I'm gonna forget to do it, I will do it now just to be on the safe side. So, for me, circular functions was a pretty easy unit, and, although it was hard to remember all of the grade 11 work from last year after I had sat it at the back of my mind for months and months, it eventually became easy again. Here are a few things to remember that might catch you on the test if you don't:

1) you CAN NOT divide by a variable because, for all you know the variable could equal zero
ex. sinx^2=4sinx
sinx=4 WRONG

sinx=0, 4 RIGHT

In this case you would have been dividing by zero which would make the answer undefined

2) If you ever come up against a question where you are substituting a variable for a function times a variable, then the variable can not be the original variable from the equation. So if you get, for example, sinx in the original equation, the variable you substitute in for it CAN NOT BE X!!!!!!

3) remember that secant is 1 over cosine and cosecant is 1 over sine

4) If the denominator of anything is 0 than it is undefined. Remember that when your answering questions on the test, if the answer is undefined you have to state it with your answer.

Well that's about all I can think of at the moment. Good Luck to everyone on the test on Friday. Oh and remember the forgetting curve ( that sounds weird) and study what we've done this unit.

Bye =)

BOB - circular functions

Well since everyone else is doing there reflection early, I guess I will too. I will first start off by saying I do not know what BOB stands for, and hopefully theres no Bob in our class that may get confused xD.

Well Circular functions was a breeze, so I'm pretty confident on the upcoming unit test this Friday. Just going to do a little extra studying before the test because we all know about the forgeting curve :).

Mr. K also made it so much easier to get my brain ready for Math, since I haven't done it for like a year. Well explained discussions on the unit circle and also his knowledge of its history.

Best advice that was probably not given by Aldrin & PJ.

-Get LOTS of sleep before the test!
-Eat Breakfast before you come to school. (Obviously because this is the morning class and your brain will probably need some fast energy to get functioning.)
-Maybe run to school if you want to get your brain pumped. (Mr.K recommends it xD)
-I'd also go over the exercises to stop that decline in the forgeting curve xD
-Remember that we like radians, and will most likely be using it a lot in the test, so be ready to remember the basic ones like: Pi/2 = 90 degrees, Pi = 180 degrees, 3Pi/2 = 270 degrees, 2Pi = 360 degrees.
-The most important one that I usually forget is to READ EVERYTHING ON THE TEST CAREFULLY. Usually you might do something like putting exact values when he wants four decimal places or something.
-Always be aware of your time during the test; skip the question if your stuck and come to it later.
-And , EVERY teacher will probably say the same thing, don't leave an answer blank!

Well I hope everyone does well on the test! Don't forget doing the BOB is worth marks on the upcoming test xD!


Well, I'm not going to go all crazy with my reflection like the first two, but yeah. I still have a lot of reviewing and notes to look over, and I don't think I'll be ready for the upcoming test. Hopefully I get the hang of this whole unit by Friday.
Considering the fact that I can't remember most of the things I learned in Grade 11 and Grade 10 Pre-Cal, this whole review with the addition of the new things we've learned really frustrated me. I don't really have a lot to say, so I guess this will be the end of my reflection? Wish me luck, and I hope I stop getting distracted. That's all.

K bye ~

Time to Reflect on the Past........

Hello to all you Pre-Calculus enthusiasts and to those visiting our blog! Good evening (or morning/afternoon depending on where you are)! I figured that I should probably do my reflection now before I forget about it later so here goes!

I'd like to start off by saying THE SCRIBE LIST IS UP! There are a few things you should know. In order to be officially crossed off the list your post must be fully completed and correctly tagged! This means that your name cannot be crossed if you say that you will when you get home. It has to actually be there and complete. Also make sure that when you tag it you put (THE UNIT TITLE), (YOUR NAME), SCRIBE. That way you get credit for doing your scribe post. (:

As far as circular functions go in our class, I feel that everything was pretty straight forward. I like the way that Mr. K lets us see where all of these numbers and formulas come from like π, sine, cosine, tangent, cotangent, etc. I think it's pretty cool how we get a math lesson as well as a history lesson! I also think Mr. K has a really great point. Instead of memorizing everything (like the sine value of 5π/6), remember the relationships like where they are in the unit circle and the root 1, root 2, root 3 pattern in the numerators in both sine and cosine. I know that's what helped me get through this unit! (:

The hardest thing during this unit was probably the grade 11 review questions. Now I know what you're all thinking. "Really? Are you serious PJ?" Why yes folks, I am dead serious. I think it's just the fact that I haven't done any streneous Pre-Calculus work in a year and that my mind is just slowly bringing everything back from grade 11 as time goes on. Well I know chemistry and physics involved some math but it wasn't like hardcore Pre-Calculus-type math. But don't worry, I'll remember eveything (eventually!) !.

So yes, I guess now is the part I should give you all advice on the test.

Don't forget any of the basic stuff like circumfrence (2πr) and area of a circle (πr^2). Haah I'm sorry if it sounds like I'm contradicting myself with the whole formula stuff and yea but sometimes there are things you should just know.

Keep the image of the unit circle in your head. Remember the relationships of sine, cosine, tangent, secant, cosecant, and cotangent. Remember SOHCAHTOA and CHOSHACAO (LOL Matthew!). That or you can remember the whole C+S pairs, like Cosine and Secant.

If a denominator has 0 it's undefined. If you have to find the square root number there are two answers (just as SheldonCooper said): one negative and one positive. If you have to solve for more than one x value and one is undefined (like sin x= 0.7384 and 2 but sin (x) can't equal 2 because it's maximum is 1), make sure that you explicitly state that.

Remember that when you have to find angles that there is usually more than one answer like for:
sin (x) = 1/2
x = π/6 and 5π/6

Of course you have to keep in mind the intervals. In my above example, my interval was [0, 2π]. If you have to solve for "all real numbers" use 'k' in your answer. For example:
Solve for 'x'. 'x' is an element of the real number set.
tan(x) = 1
x=π/4 + kπ where 'k' is an element of the integer number set

Don't panic! Stay relaxed and don't fret if you can't get the answer right away. Skip it and move on. It'll come to you eventually.

Take your time! Don't rush! Double check your answers and make sure you did everything right. There's no harm in checking your work. In the end it'll probably be beneficial for you!

Well I think this post is getting a little bit too long. I won't actually be in the room doing the test with all of my wonderful classmates as I, along with Dion and Rebecca will be at S.E.T. that entire day. We still wish you all the best of luck on the test! We're with you guys in spirit! xD

BOB - as it was called in past years

Hey everyone ! Allow me to preface this post by saying that this is a very good class and Mr. K. has an exceptional way of teaching. I understand that one should create a blog post prior to Circular Functions Test, so I just wanted to create mine now since all yall can read this stuff one day earlier rather than just the day before the actual test.

Anyways, this unit is almost over and I'm confident. At my first encounter with this unit, I was appalled and just disgusted, which is way of saying “Oh my gosh! How am I supposed to do this?!?” This was last summer though, so I immediately gave up. I actually tried being diligent back then, and now, I plan to remain diligent.

Anyways, comprehending the unit circle was not such a laborious task to me. The pattern is very self-evident. Mr. K. had helped elucidate several math concepts. Nevertheless, I do have the propensity to make silly mistakes. Other than that, I am fairly prepared, but I am still going to study to ensure that I am at my best.

So here are some things that hopefully aid you on the test. In addition, I know that this is basic mathematics and is common sense, but people get stressed out and forget the easiest things, which consequentially leads to mistakes. So these are my efforts to help.

Area of Circle = πr^2
Circumference of a Circle = 2πr, πd

When the denominator is zero, the answer is undefined. For example, Tan(π/2)= 1/0 , therefore, undefined. Another example is Csc(π) = 1/sin(π) = 1/0, therefore undefined.

Remember that Mr. K wants your work to be written in a vertical manner and that if there is no solution or the answer is undefined, state it.

When obtaining the square root, two values can be achieved. The square root of 4 = ±2. Do not forget that. Another example is R^2 = S + T. Therefore R = ± squareroot of (S + T) .

Here is another common mistake. (sin x)(tan x) = (sin x) A rational thing to do would be to isolate tan(x) to equal 1. However, that only obtains a partial bit of the actual answer. What you do is transpose sin(x) from the right side to the left side. After that, you factor out sin(x) which results in sinx(tanx – 1) = 0.

Cosx and sinx has a range of [-1,1] . Anything less than -1 or greater than 1 leads to "undefined"

DABC – mnemonic for parameters

Round to a minimum of 4 decimal places yall when necessary.

If you finished all of your exercises, review them. If you didn't finish them, go do them!

Check out some Youtube videos, past Precal Blogs, other websites, that online course website (merlin), and PC40s Mb site.

Good luck and ask questions if you have any problems.

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 accessed 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.

IMPORTANT: Make sure you label all your Scribe Posts properly (Your Name, Unit Title, Scribe) or they will not be counted.

Cycle 3Probably the last cycle!

D-S Skyline

Mr Lollipop

~Pokemon Champion~
Laikus the Ficus


Tuesday, February 17, 2009



hey guys! It's mary here and as your scribe from yesterday, i'll be summarizing the wonderful moments of precal Sorry about leaving you with that cliff hanger last night. But as promised, i will finish the post.

For yesterday’s class, we learned..
~ What the sine and cos graphs looks like and why the way it does.

~ The difference between the sine and cos graph, along with the meaning of amplitude and period.
~ What a sinusoidal axis is.

~ The 4 ways you can alter a sine or cos graph. (Translations)

Sine Graph:
wow, the image quality sucks. LOL bare with me!
Okay, so in order to explain the graph, you must understand the unit circle. As you go around the unit circle, starting from zero(or 2/pi), the sin value increases than decreases. The Sine value goes from 0, 1, 0, -1, and back to 0 again as it makes it full circle. It has a max value of 1 (when reaches /pi/2, and a min value of -1 (when reaches 3/pi/2).Regarding the unit circle, the sine graph displays the sine values as you travel around the unit circle, in a way where we can see that pattern. (of 0, 1, 0, -1, 0). This means the y-axis on the graph shows the sin value, while the x-axis shows the distance traveled on the unit circle. (2/pi, /pi/2, /pi, 3/pi/2 etc). Understanding this would come in handy when asked to draw a sine graph. 10 points for those who can understand the relationship! (brownie points) if not, ask yourself this: "where does sin equal zero on the unit circle?" look at the sine graph, "where does sin equal 1 and -1 on the unit circle?" then look at the graph. Your answers should be the same as the answers on the graph. "zero,2/pi, /pi, /pi/2 and 3/pi/2".

1b) Cosine Graph
Again, just like with the Sine Graph, the y-axis on the graph shows the cos value, while the x-axis shows the distance traveled on the unit circle.

2a) Sine Graph vs. Cosine Graph

The Sine Graphs and the Cosine Graphs are pretty much the same. The only difference is, cos is horizontally shifted, /pi/2 units to the left, on the x-axis, from the sine graph . This means, if you were to take a Sine Graph, and push it /pi/2 units to the left, you would have a Cos graph. And if you were to take a Cos Graph and pull it /pi/2 units to the right, you would have a Sine graph. "They are identical in amplitude, period, domain and range". I hope you guys can understand the picture below. I was trying to show you visually that the two graphs are /pi/2 units away from each other.

2b) UH OH, new terms?! don't worry, i got this! ;)

mary says:
whats Period and Amplitude again? -__-

pj says:
Period is how long it takes for 1 cycle to repeat

pj says:
Amplitude is the distance from the highest points to the average

mary says:
so 2pi?

pj says:
it's 2pi for the regular sine/cosine curve


Sinusoidal Axis: "Sinusoidal axis: is the line which passes directly through the center of the sin curve horizontally. This line is always parallel to the X axis if it is not the X axis to begin with." The sinusoidal axis is used as a reference line when altering your sin or cos graph. Remember, its not actully part of the graph, so don't draw it on a test, unless told to.


3a) Translation:
When graphing trig functions, there are four ways it can be altered. (from its regular form, sin(x) or cos(x).)
Shifting it up/down. (vertical shift)
Shifting it left/right. (horizontal shift)
Stretching it vertically.
Compressing it vertically.

~Vertical shift (Shifting it up/down) this would go the same for cos and sine

example: (because its more effective than me blabbing away) sin(x)-2
the negative 2 would move the max and min values, of the graph, two units down. Another way of looking at it, would be having the new sinusoidal axis two units down from the previous. In this case, the sinusoidal axis would go from 0 (x-axis) to -2. Then you would just draw the graph as you would from the new sinusoidal axis.
example: sin(x)+2
Just like before, but the positive 2 would move the max and min values, of the graph, two units up.

~Horizontal shift(Shifting it left/right) this would go the same for cos and sine
example: sin(x-2)
the negative 2 would move the of the graph, two units right, from the regular sin graph. Notice how i said right, not left.

example: sin(x+2)
the positive 2 would move the of the graph, two units left, from the regular sin graph.

~Stretching&Compressing it

example: sin(2x). sin(1/2x)
The 2 would compress the graph, twice as much. While the fraction, 1/2, would stretch it twice as much.

3b) Translation order; DABC!
Most of the time, you will be faced with a combination of these translations. (vertical/horizontal shift, compress/stretch). And there is a order you go by, when you have to draw them. D A B C

From AsinB(x+C)+D or AsinB(x-C)+D, you would use DABC. Meaning you would do the vertical shifts first, since D is first in order.

Okay, enough of the snore-fest!

1) Mr. K will not be in class for the rest of this week, and the following week after. Reason: because of a family emergency. But show no fear,(that one was for you pj!), Mr. k had said he’ll keep in touch with us through the blog, and I'm sure everything will work out with Mr. K's situation.
2) Also, there is still an unit test on Friday, FEBRUARY 20th. Study hard and good luck :D

Next scribe will be laika~

Today's Slides: February 17

Here they are ...

Friday, February 13, 2009

Happy Valentine's (Approximation) Day! >:D

Hello there mon internet (stalker) classmates! It's ANNabanana here! Right now I am very tempted to say that all we did today in class was math.


Anywho, we started off the day with a little mental math. You know, the unit circle stuff our mental math's have been based on all week (click here if you need some practice with it). Then we went into small groups so our brain waves could be shared to solve the problems that were on the smartboard. If you would dare to look at Mr. K's slides you'll see what problems I'm talking about. Rather simple trigometric functions, it's just that I have to point out some things to you mon dearies. :D

I'd like you're eyes to be entranced by the slide directly below this.

You see that big red X? Well Mr. K showed us the wrong way to solve equations. Never ever ever EVER divide by a variable because you don't know the value of it and might potentially be zero. When you divide by zero the answer becomes undefined and you don't want that! Talking about undefined...

Why would I point this out? Because I had such a wonderful time writing out the (wrong xD) answers on the slide it was from. No, actually Mr. K pointed out that on our exam we have to write the answers that don't work or that are undefined seperate from the answers that DO work. Also, for those of you wondering why cos x = 2 is undefined, it's because the unit circle has a radius of one and the maximum unit that it can go up to is one. Two unfortunetly is too big. D=

Here's something new. Let's look for the answer in the domain of.. what's this! The set of real numbers?! Oh my! There are infinite answers for this question! How can we possibly write them all down?!?
It all comes down to k. A number in the set of intergers. Something that tells you how many times it goes round and round (with pi). For any tangent say that the answer is (tan x) + k(pi) because every tangent is an unit of pi (half a circle) away from eachother. For all other answers it should be (your answer here) + 2k(pi) because it's going to take one whole revolution around the unit circle to reach that answer again.

The homework for the weekend is the rest of exercise 5 and the last 10 quesitons on exercise 6.

LOL, look what I found on youtube.

Hmmmm... let's see. The next scribe is Mary. :D

"Insert math quote here"

Today's Slides: February 13

Here they are ...

Thursday, February 12, 2009

The Life of π

Hii bloggers, this is Rebecca your scribe for the evening.

In today's class we talked about solving trigonometric equations larger than 2π.
We began the class by reviewing some of the algebraic questions from yesterdays class.

I believe we were then called down to the MPR for our biannually assembly. At the assembly we were told how wonderful we were and how to become even more wonderful! If you are confused about school rules and missed this assembly speak to a teacher and I'm sure they will help you. :p

So back to math class...
We were then asked to solve the following questions. Mr. K took a few minutes telling us how our calculators were stupid and only told us one answer to a question and how since were smarter than the average bear we need to find the other angles. He then told us that later we will learn our calculators weren't actually lying to us, but we wont worry about that in this unit.

One question we had while answering this question was "Couldn't you also have -π/6?" The answer was no because it does not fall in the interval.

Next we did some fun mental math. (sorry for my poorly drawn paint pictures but the equation writer was not cooperating!)

When doing these types of questions think about where in the unit circle you are. For example for cos 13π /3 you are in quadrant 1. This means your answer will be positive because x is positive in quadrant 1.

Some side notes:

  • Mr. K told us that if you have something that is tedious to rewrite you can use substitution. Always show what you are substituting at the top of your page. You can use a letter (NEVER USE X) from any alphabet or a symbol.
  • Always go to 4 decimal places for this class!!

Homework for today was exercise 5, questions 11-20. Good luck!

Last but not least tomorrows scribe will be Annabanana!! :D

Today's Slides: February 12

Here they are ...

Wednesday, February 11, 2009

(8) I Wanna Be, The Very Best... NOT!

Math-ew's Super Awesome Scribe Post

Hey Pre-Cal 40-S Winter 2009! This is Matthew Aka Pokemon Champion (though apparently Mr. K's son may have something to say about that... bring it Mr. K Junior... Just kidding =D)

Anywayyyyys... today we started off class with Mr. K very likely confusing or scaring our parents by implementing use of the "yackpack" tool on the blog. he first announced who we were ( We come in peace?) and then we all just sorta started to laugh, and now some of our parents are wondering why they are suddenly the stars of a latest sitcom ( My Child the Precal Student, perhaps?)

Ah, but I digress, back to the math! After our excitement died down a bit, the slideshow appeared, in all it's magical Smart Board glory. A very similar premiere slide appeared today, now with a new caption. Today we were to delve into the wonder that is solving trigonometric equations! (really this time).

We started out with some fairly simple questions reminiscent of the day before. Determine trigonometric values and come to an exact value as an answer. Here are the questions along with some straight-forward solutions.

Something Mr. K touched upon was the concept that we don't exactly NEED to rationalize the denominator anymore as far as radicals go. No matter where you put the radical, it's still there. and sometimes it's probably even more handy to eliminate radicals from the numerator and have them all on the denominator, but I used the answer where we do rationalize radicals in the denominator. Heavy stuff...

We then had a bit of a mental math jamboree! Or, just a mental math quiz, about SohCahToa/ChoShaCao of certain angles. It was out of 10 and it seemed like a big problem was the last question resulting in an answer of "undefined". Always make sure to check when you have 1/0 or 0/1 because their meanings are quite different..

Yesterday we had also started to talk about phi, or if the symbol interests you at all. Phi as a refresher, is just another fun Greek letter/symbol (huzzah for the Greeks!) meaning the related angle of "theta". Today we started investigating the use of it a little bit more.

Now we started doing questions using the inverse, or arc, trigonometric functions. For each given value, we should end up with 2 different angles (except of course, in the case of 90,180.270, and 360 degrees.) To spice things up a little bit - solving for the angles in radians. I won't bother with the first question of the type because it's basically a question we all know and love using a common sin value on the unit circle. For those who need it, the answers result in Pi/4 or 3Pi/4.

It was after this question that "Phi" came in.

Here are the 2 questions we solved using phi:
Next up, we took a look at some good old fashioned algebraic equations.These should have been easily solved, and were somewhat of a break from the slightly more difficult concepts we are trying to grip now. Checking the slide for this one should be more than enough of a refresher for everybody, but i put it here as well just in case. Our last slide for the day was almost a carbon copy of this one except now it incorporated trig functions. Now (trig function)x= 1/2 or 1/3 rather than just x. These questions are solved in the same way as with the phi questions previously shown. Rather than give you the answers here, i think it would be quite prudent for you all to just try to figure the last slide out combining our knowledge from slides 4 and 5 with slide 6 and seeing what you can do as far as that goes.

Last bits of info! Today Mr. K taught us a handy trick to do with our TI-83/84 calculators ( as well as revealing the secret of the almighty TI-89, but let's not get too excited). After you have some sort of number you want stored into memory, you can press the STO key, then the GREEN ALPHA KEY followed by a letter of your choice (although X is NOT advised due to its use in other areas in the calcualtor). He then went on to tell us that our entire calculators will be wiped before the exam and that, not even our fun puzzle games would survive... tear tear :(
Homework for tonight was Exercise 4 Q's 1-10, and any 5 of the last 10.
It was also suggested that we draw unit circles and to use lots of colour. He mentioned how important colour is and how it can help us remember things, such as how we recognize yellow early on but not to rely on it because its a very bright and hard to read colour. Anyways sorry for the lateness.... REALLY lateness... Computer kept freezing up and had no notes so kind of had to wing it.. But excuses are lame and i'll try to manage my time better next time. Hopefully This helped some people out... it wasn't as awesome as I intended it to be but what can ya do?
NEXT SCRIBE ISSSSSS: *unnecessary drum roll* REBECCA!!! Congratz!! XD Good night every one, and happy mathing! =D

Today's Slides: February 11

Here they are ...

Tuesday, February 10, 2009

Scribe For the Day

Hey guys, it's j.L (John) here and yeah I just got off work and I'm tired.... So, I'm going to make this post as quick and painless as possible.

Well, we started off by talking about a grade 12 Mental Math Contest with prizes totalling up to 5000 dollars, if i remember correctly. Most of our class is grade 11's anyways, so most of us are going to take it next year, like me. Well i think i strayed off topic too much, back on to the real task.

So basically this picture is a triangle, which ray intersects a point on the unit circle. I already figured out the hypotenuse by the old Pythagorean Theory. Since I found out the hypotenuse, I can use a ratio to figure our what points the ray intersects the unit circle, Shown in the picture below:

Oh and also we learned the related angle of "theta" is know as "phi. After this stuff, we had a QUIZ "oooooooOOOOoooooo" "ahem".... Questions and answers are below:

So that was our dreaded quiz of the day. Oh and don't sleep in late for Mr K's classes or he will come to your house. Well I'll end this by choosing my next scribe and I CHOOSE YOU MATCHU a.k.a POKEMON CHAMPION (or his mortal name = Mathew). Later folks. Oh and haha maxed out again, nice job guys.