Reflection

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.

-Stephen

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).

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

Reflection

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!

PRETEST

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

http://img11.imageshack.us/img11/5710/pretestcircularm.gif
http://img3.imageshack.us/img3/7052/pretestcircular2.gif

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.

BTW

WHO IS BOB?!

Reflection

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.

bob

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 ....

Pretest Circular Functions

View more presentations from heviatar. (tags: pc40sw09 circular)

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^2=4sinx
sinx(sinx-4)=0
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!

reflection

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

UGHH DABC!

EDIT~

3.14159..

hey guys! It's mary here and as your scribe from yesterday, i'll be summarizing the wonderful moments of precal class...today. 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)




1a) 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.

ALMOST DONE, STAY WITH ME GUYS!

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!

IMPORTANT NOTICES!
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

Resources:
http://www.cbv.ns.ca/mathhelp/P66.htm
http://www.clarku.edu/~djoyce/trig/
http://www.fooplot.com/

Next scribe will be laika~