My Turn to Scribe 2 ~ HOOOOOOOOOO!
It was my turn to scribe so...
At the start of class, Mr. K started by showing us a few websites with varying purposes. First he showed us skrbl.com which is basically an online whiteboard. Then he presented twitter.com which you can use to communicate with people but you have to sign up with an account.
After viewing the features of those sites, we finally got to buckle down and write our Pre-test. It was basically a scaled down version of a normal test. There were 2 multiple choice, 2 short answer, and 2 long answers. We were alloted 15 minutes. After our time limit was up, we assembled into groups of about 3 people. Each group would have to hand in the a paper with the best possible solutions. Following that we went over the answers to the test. Bell Rings*
ＴＨＥ END。
The next scribe is kristina.
Showing posts with label Circular Functions. Show all posts
Showing posts with label Circular Functions. Show all posts
Tuesday, February 26, 2008
Circular Functions BOB
Hello, hello again. I'm back to do some.. BOB-ing. Does anyone else find it strange that you call it BOB? Or maybe that's just me.. Anyways..
I think this unit, for someone who hasn't touched any math for a YEAR, was a pretty good unit to start with. I'm not saying it was easy, but it was simple enough that I was able to wrap my math-challenged mind around it, and that was more than awesome. I found that having the unit circle forever drawn in my head really helped me; to me, having that down is understanding everything else.
But what I'm really worrying about is the graphing, because I missed the classes that focused on it. But I am getting it, just reaally slowly, kind of like Jamie, but.. probably slower.
Soo, that's my BOB for Circular Functions. Good luck on the test tomorrow you guys. =)
I think this unit, for someone who hasn't touched any math for a YEAR, was a pretty good unit to start with. I'm not saying it was easy, but it was simple enough that I was able to wrap my math-challenged mind around it, and that was more than awesome. I found that having the unit circle forever drawn in my head really helped me; to me, having that down is understanding everything else.
But what I'm really worrying about is the graphing, because I missed the classes that focused on it. But I am getting it, just reaally slowly, kind of like Jamie, but.. probably slower.
Soo, that's my BOB for Circular Functions. Good luck on the test tomorrow you guys. =)
Monday, February 25, 2008
BOB, Circular Functions
Well the unit Circular Functions was a bit confusing for me in the beginning because of that whole converting degrees to radians it took me a week to understand it but now i get it. another thing that also confused me was the functions secant and co secant it confusted me because the words do not match haha but i get it now. Now the only thing that is troubling me is the graghing for some odd reason i get confused with the period part (B) in DABC another thing that i need to remmember is to put label my graph and also put arrows on my graph. The part that i liked about this unit is that you wont lose any marks for forgeting to put the untits for radian, because there are no units ahaha.
Well now i guess its time to study for the test on wednesday.
Richard
Well now i guess its time to study for the test on wednesday.
Richard
BOB on Circular Functions
Now that there's a test, I'm slightly nervous, but anxious to get it over with. This unit at first was quite simple and straight forward because converting degrees to radians in respect to proportions is quite easy.
The unit circle however, was really annoying because of all the memorizing we had to do. We had to memorize each point for every radian measurement on the unit circle, but everything in math is a pattern, and as soon as you have the pattern etched in memory then it should be no problem memorizing things such as the unit circle. I still sometimes have trouble with the points because I have yet to memorize it all. In time I will though. I guess I should draw out the complete unit circle a couple times without any outside help such as notes.
The next part I found worth mentioning is the trigonometry equations, we did these in grade 11, and I remember these quite well. I believe these equations were introduced to us in preparation for the sine and cosine waves that we are currently working on. Found from the equation f(x) = AsinB(x-C)+D or f(x) = AcosB(x-C)+D. Sure, it may look hard at first but with all great puzzles, you must put it together piece by piece. Plotting each value in order. Preferably in the order DABC. I found that plotting these were not too much of a hassle but I have yet to perfect it, due to simple mistakes. In time I will get wiser though.
Well that just about sums up my understandings on the unit of circular functions. All in all, this unit was a little rough around the edges, but still understandable.
Until next time!
-Francis
The unit circle however, was really annoying because of all the memorizing we had to do. We had to memorize each point for every radian measurement on the unit circle, but everything in math is a pattern, and as soon as you have the pattern etched in memory then it should be no problem memorizing things such as the unit circle. I still sometimes have trouble with the points because I have yet to memorize it all. In time I will though. I guess I should draw out the complete unit circle a couple times without any outside help such as notes.
The next part I found worth mentioning is the trigonometry equations, we did these in grade 11, and I remember these quite well. I believe these equations were introduced to us in preparation for the sine and cosine waves that we are currently working on. Found from the equation f(x) = AsinB(x-C)+D or f(x) = AcosB(x-C)+D. Sure, it may look hard at first but with all great puzzles, you must put it together piece by piece. Plotting each value in order. Preferably in the order DABC. I found that plotting these were not too much of a hassle but I have yet to perfect it, due to simple mistakes. In time I will get wiser though.
Well that just about sums up my understandings on the unit of circular functions. All in all, this unit was a little rough around the edges, but still understandable.
Until next time!
-Francis
Jamie's First BOB
Hello universe, and hello there BOB...I think everyone's introduced. I see from previous posts, everyone knows BOB.
There's an upcoming test this week and the normal thing is to be nervous. But I'm not normal, I'm just something else..and if you're something else, you can have different feelings like anxiety and quivering in fear. But what way better to review than to talk about what was learned in the past month or so?
The first unit was about Circular Functions. Functions about Circles...that's just plain cool. Radical, really. and round.. I just like making the "R" sound....TORRRRRRRRRRRRRRRRRRRRRTILLA nailed it! But yes, no more tangents. This unit was a great introductory unit, and it made me feel better about myself because I felt so smart coming up with answers out of no where but that was the beginning. It was basically a review of grade 11 pre-cal, from where i just freshly sprung from last semester...We took "rules" like CAST and disregarded them-- REBELS!! and we took theories apart and properly determined the difference between an equation and a proportion.
BUT THERE IS ONE SLIGHT PROBLEM that might just lead to my demise in the near future. I am a SLOOOOOOW learner. Or as benofschool used to say, "as swift as a turtle"...actually slower than that. A sloth. I just have a problems with prioritizing [spelling?] thoughts in my head. I know the most random of things, like the lyrics to any Sweeney Todd song or how to talk in different accents, but I still can't grasp the whole idea of the unit circle and the DABC concept. Don't get me wrong, I know it and where the information comes from and understand it, it's just I can't register these values fast enough to finish a test!!!! URGH!!! I'm not making any excuses like a scapegoat, but I'm just saying I can do it...in about a century. The funny thing is, my magic number is not 6. It's more like 6, 295,048...I know I'm overexaggerating, but I'm getting the point across. I'm even trying a new thing [the idea came from the walkie talkie device on the blog] where I recorded myself singing the sincostan values in quadrant one and then making my way across all of the quadrants because I believe music is my TOOL. Yes, I try to be innovative you know....also modest, but I suppose I'm not doing a great job at that.
OKAY YES...Mr. K. did say to not MEMORIZE but REMEMBER...but sometimes I just the provided example to the idea of the paradox, FORGET TO REMEMBER. Here I was last year being told that the "VERTEX WAS EVERYTHING", but now it's more like "IF YOU DON'T KNOW THE UNIT CIRCLE, YOU WILL FAIL." How encouraging. and the PARAMETERS!!! for graphing these functions. But I promise to you world, BOB, and myself that I will master the art of circle-- THE ROUND SENSEI.
By the way, good luck on your tests everyone! Let's count down to it like it's another New Years DAY! Don't mind my being nutty, it's just I'm trying to think of the glass being half full right now. hahah
There's an upcoming test this week and the normal thing is to be nervous. But I'm not normal, I'm just something else..and if you're something else, you can have different feelings like anxiety and quivering in fear. But what way better to review than to talk about what was learned in the past month or so?
The first unit was about Circular Functions. Functions about Circles...that's just plain cool. Radical, really. and round.. I just like making the "R" sound....TORRRRRRRRRRRRRRRRRRRRRTILLA nailed it! But yes, no more tangents. This unit was a great introductory unit, and it made me feel better about myself because I felt so smart coming up with answers out of no where but that was the beginning. It was basically a review of grade 11 pre-cal, from where i just freshly sprung from last semester...We took "rules" like CAST and disregarded them-- REBELS!! and we took theories apart and properly determined the difference between an equation and a proportion.
BUT THERE IS ONE SLIGHT PROBLEM that might just lead to my demise in the near future. I am a SLOOOOOOW learner. Or as benofschool used to say, "as swift as a turtle"...actually slower than that. A sloth. I just have a problems with prioritizing [spelling?] thoughts in my head. I know the most random of things, like the lyrics to any Sweeney Todd song or how to talk in different accents, but I still can't grasp the whole idea of the unit circle and the DABC concept. Don't get me wrong, I know it and where the information comes from and understand it, it's just I can't register these values fast enough to finish a test!!!! URGH!!! I'm not making any excuses like a scapegoat, but I'm just saying I can do it...in about a century. The funny thing is, my magic number is not 6. It's more like 6, 295,048...I know I'm overexaggerating, but I'm getting the point across. I'm even trying a new thing [the idea came from the walkie talkie device on the blog] where I recorded myself singing the sincostan values in quadrant one and then making my way across all of the quadrants because I believe music is my TOOL. Yes, I try to be innovative you know....also modest, but I suppose I'm not doing a great job at that.
OKAY YES...Mr. K. did say to not MEMORIZE but REMEMBER...but sometimes I just the provided example to the idea of the paradox, FORGET TO REMEMBER. Here I was last year being told that the "VERTEX WAS EVERYTHING", but now it's more like "IF YOU DON'T KNOW THE UNIT CIRCLE, YOU WILL FAIL." How encouraging. and the PARAMETERS!!! for graphing these functions. But I promise to you world, BOB, and myself that I will master the art of circle-- THE ROUND SENSEI.
By the way, good luck on your tests everyone! Let's count down to it like it's another New Years DAY! Don't mind my being nutty, it's just I'm trying to think of the glass being half full right now. hahah
Monday, February 25
MY TURN TO SCRIBE ~ HOOOOOOO!
It was my turn to scribe so...
First of all, we started out by going over the test about maximum area of a triangle. So we have point P on the unit circle. B on the x-axis and it has to be a right angle triangle. What's the maximum area? Well we know that the area of a triangle is base x height divided by 2 and the base and height is equal to the x and y components of the triangle. We also know that the x and y components are equal to the sine and cosine of the central angle. We tested out the values and found that as the angle goes up the area would also increase but after π/4 radians the area would go down again. That means the sine and cosine of π/4 radians will give up the largest area.
After that, we went over question N on the sheet. Turns it out it was not a typo and we actually had to factor out the 2 pi. This will give us a period of 1. After that we went over some more transformations and Ｉ a few important things we should know. For example, parameter B is not the period itself, but actually helps us calculate the period. If we substitute B in the formula: period = 2π/b. Another important tip we should know is if we are given parameter A = -1/2 and we are asked for the amplitude, then the answer would be 1/2 and not -1/2. This is because the amplitude is the distance from the sinusoidal axis to the maximum or minimum points. Therefore, distance cannot be negative because this would destroy all logic. In other words, read your questions carefully, if it asks for amplitude, then discard the negative sign but if it asks for the value of parameter A then you include the value of A.
A few minutes later, we were given a wave graphed on the Cartesian Plane and were asked to write the equation of the graph in sine and cosine. Turns out there are INFINITE ways of writing the equation so... there's nothing to complain about there and plus we will only be required to only write one or two (max) equations on tests and the provincial exam.
Somewhere in the class, we looked at the infamous tangent function. Finally after a few of us were dying to see it, it was revealed. The tangent function is kinda special. It appears to be like x³ but IS NOT. The curvature is slighty different. Another feature of the wonderful tangent functions is asymptotes. Asymptotes are areas where tangent cannot exist. Since tangent is a trigonometrical function it has to do with triangles. At certain angles, tangent does not form a triangle therefore tangent cannot exist. Tangent can also be infinitely large unlike sine and cosine which are confined to -1~1.
That pretty much wraps up the class. Until next time.
It was my turn to scribe so...
First of all, we started out by going over the test about maximum area of a triangle. So we have point P on the unit circle. B on the x-axis and it has to be a right angle triangle. What's the maximum area? Well we know that the area of a triangle is base x height divided by 2 and the base and height is equal to the x and y components of the triangle. We also know that the x and y components are equal to the sine and cosine of the central angle. We tested out the values and found that as the angle goes up the area would also increase but after π/4 radians the area would go down again. That means the sine and cosine of π/4 radians will give up the largest area.
After that, we went over question N on the sheet. Turns it out it was not a typo and we actually had to factor out the 2 pi. This will give us a period of 1. After that we went over some more transformations and Ｉ a few important things we should know. For example, parameter B is not the period itself, but actually helps us calculate the period. If we substitute B in the formula: period = 2π/b. Another important tip we should know is if we are given parameter A = -1/2 and we are asked for the amplitude, then the answer would be 1/2 and not -1/2. This is because the amplitude is the distance from the sinusoidal axis to the maximum or minimum points. Therefore, distance cannot be negative because this would destroy all logic. In other words, read your questions carefully, if it asks for amplitude, then discard the negative sign but if it asks for the value of parameter A then you include the value of A.
A few minutes later, we were given a wave graphed on the Cartesian Plane and were asked to write the equation of the graph in sine and cosine. Turns out there are INFINITE ways of writing the equation so... there's nothing to complain about there and plus we will only be required to only write one or two (max) equations on tests and the provincial exam.
Somewhere in the class, we looked at the infamous tangent function. Finally after a few of us were dying to see it, it was revealed. The tangent function is kinda special. It appears to be like x³ but IS NOT. The curvature is slighty different. Another feature of the wonderful tangent functions is asymptotes. Asymptotes are areas where tangent cannot exist. Since tangent is a trigonometrical function it has to do with triangles. At certain angles, tangent does not form a triangle therefore tangent cannot exist. Tangent can also be infinitely large unlike sine and cosine which are confined to -1~1.
That pretty much wraps up the class. Until next time.
Sunday, February 24, 2008
BOB; Circular Functions
So knowing there's a test this week. I'll be BOBing.. while bobbing my head to music. Okay, lame, I know.
To the point. We started the semester without even introducing ourselves and our names which was a definite change from other teacher's ice breaking activities. And of we started, learning about Radians and what not, converting from degrees, a measurement we've been using in pre-cal for how long now, and finding our measurement was 'x' number pi over 'x' number. At first I had a hard time grasping the concept but later became comfortable after studying it for a while.
Later on, we learned the Unit Circle and all the radian measurements around the circle. Yet another item to remember, and the words of consequence from Mr. K when we questioned the idea of failing to memorize such a thing and he put it out plainly "You'll fail." And that's how the Pi pie crumbles... or is it how the cookie crumbles. Okay whatever, I'll stop with the mediocre attempts at what's called a joke. After much practice, I became comfortable with the Unit circle. Then finding the arc length was something else as well as we found that no matter how stretched out from the origin, it still shares the same proportionality.
The waves I found I was having a little trouble but had an easier time understanding than the whole Unit Circle memorization task. The only trouble I really had was with the Period ('B') but after Ben showed me how to do it it became clearer. I'll definitely study for this bad boy... Lol
G'niight all and good luck on the Test. Remember, the apple doesn't fall from the tree... wait what does that have to do with anything...?
-Lawrence
To the point. We started the semester without even introducing ourselves and our names which was a definite change from other teacher's ice breaking activities. And of we started, learning about Radians and what not, converting from degrees, a measurement we've been using in pre-cal for how long now, and finding our measurement was 'x' number pi over 'x' number. At first I had a hard time grasping the concept but later became comfortable after studying it for a while.
Later on, we learned the Unit Circle and all the radian measurements around the circle. Yet another item to remember, and the words of consequence from Mr. K when we questioned the idea of failing to memorize such a thing and he put it out plainly "You'll fail." And that's how the Pi pie crumbles... or is it how the cookie crumbles. Okay whatever, I'll stop with the mediocre attempts at what's called a joke. After much practice, I became comfortable with the Unit circle. Then finding the arc length was something else as well as we found that no matter how stretched out from the origin, it still shares the same proportionality.
The waves I found I was having a little trouble but had an easier time understanding than the whole Unit Circle memorization task. The only trouble I really had was with the Period ('B') but after Ben showed me how to do it it became clearer. I'll definitely study for this bad boy... Lol
G'niight all and good luck on the Test. Remember, the apple doesn't fall from the tree... wait what does that have to do with anything...?
-Lawrence
My BOB for Circular Functions
The test is coming up soon so I thought the time was ripe for a BOB. Our very first unit is circular functions. At first, it was relatively easy. Nothing too difficult, I would say it was exactly like Grade 11 but units in radians instead of degrees. Took me a while to adjust to radians since we have been using degrees for most of our lives but as Mr. K always proclaims "FRACTIONS ARE OUR FRIENDS". Casting away CAST took zero effort whatsoever. As so, the memorization of the unit circle. Since it always has to be a root of 1, 2 or 3 over 2. Converting radians to degrees and vice versa was cakewalk since setting up a proportion is easy for me. All thanks to my Grade 8 Math teacher: MR. TRAN!
As things progressed on, we were exposed to more things that I found familiar from Grade 11. For example, solving for trigonometry functions of X was one of them. The only difference is that the angles are in radians now. Another thing was sine and cosine waves and their transformations.
I liked a few things about this unit. The fact that radians have no units was a load off my mind (in case I forget to write the unit on a test and lose a 1/2 mark). Solving for exact values of stuff was also enjoyable.
That brings my BOB to an end. Good night and Good Luck!
As things progressed on, we were exposed to more things that I found familiar from Grade 11. For example, solving for trigonometry functions of X was one of them. The only difference is that the angles are in radians now. Another thing was sine and cosine waves and their transformations.
I liked a few things about this unit. The fact that radians have no units was a load off my mind (in case I forget to write the unit on a test and lose a 1/2 mark). Solving for exact values of stuff was also enjoyable.
That brings my BOB to an end. Good night and Good Luck!
BOB: Circular Functions
Hello everyone, since the test for circular functions is supposed to be this week, I'm here doing my BOB.
Okay, so during the beginning of this unit, when we were just introduced to converting degrees to radians and whatnot, I found that this was really easy. Sure, it was a bit confusing at first since I wasn't used to working with radians but it eventually got better as the unit progressed. Now I actually like working in radians better than degrees!
One part I had trouble with AT FIRST was learning the unit circle. As soon as I saw all those numbers on that unit circle, I panicked. What made it even worse was when Mr. K told us that we had to memorize EVERYTHING that was on the darn thing, and at that point, I was ready to cry. It didn't help much when Roxanne asked him what would happen if we didn't memorize the thing by the time he told us, to which he answered "You'll fail." But now that I know the cursed thing that caused me so much pain, I feel much better.
Now onto the graphing bits. The basic graphing wasn't so bad, but the added stuff, such as DABC, was. Sure, DABC was fun to say, but it was hard to understand at first since the last part of that class was rushed and it was so much to absorb in just those last 2 minutes we had.
Um, yeah, that's all I've got to say for this unit. It had its hard and easy moments, and overall, it was pretty good. That is all.
Okay, so during the beginning of this unit, when we were just introduced to converting degrees to radians and whatnot, I found that this was really easy. Sure, it was a bit confusing at first since I wasn't used to working with radians but it eventually got better as the unit progressed. Now I actually like working in radians better than degrees!
One part I had trouble with AT FIRST was learning the unit circle. As soon as I saw all those numbers on that unit circle, I panicked. What made it even worse was when Mr. K told us that we had to memorize EVERYTHING that was on the darn thing, and at that point, I was ready to cry. It didn't help much when Roxanne asked him what would happen if we didn't memorize the thing by the time he told us, to which he answered "You'll fail." But now that I know the cursed thing that caused me so much pain, I feel much better.
Now onto the graphing bits. The basic graphing wasn't so bad, but the added stuff, such as DABC, was. Sure, DABC was fun to say, but it was hard to understand at first since the last part of that class was rushed and it was so much to absorb in just those last 2 minutes we had.
Um, yeah, that's all I've got to say for this unit. It had its hard and easy moments, and overall, it was pretty good. That is all.
BOB: Circular Functions
Since our test will be sometime this week, I decided to make my BOB entry before I forget. =)
In the beginning of this unit, I wasn't so comfortable converting degrees to radians. Up and till this unit I've always been using degrees but later in this unit, it became easy. This unit wasn't as bad as I thought it would be because from last year's precal I had trouble with circular functions. Now, I understand how to figure out certain word problems and convert degrees into radians and vice versa. I also found that finding the sine, cosine, and tangent of angles are pretty easy and it's probably because of the mini quizzes we had. But finding cosecant, secant, and cotangent can be a bit confusing at times and may take up a bit of time for me to figure out. What helps me a lot is to look for patterns to solve different kinds of questions which makes it much easier to do.
On the other hand, considering the fact that I missed a couple classes last week, I was a bit confused with the graphing we had to do. At first I was like, "what is this?" But after a few explanations and practicing doing questions I got the hang of it. Remembering DABC actually helped me a lot to do the problems. Yet, I'm not totally comfortable with graphing because it probably takes me more time than others in the class.
In conclusion, this unit was "OK" and I hope I do well in the first test as well as everyone else. With that said, goodluck to everyone!
PS..were we taught the graph for tangent when I wasn't here? Because in excercise 6, I believe there is a question about it and I didn't know how to do it?! Help?
In the beginning of this unit, I wasn't so comfortable converting degrees to radians. Up and till this unit I've always been using degrees but later in this unit, it became easy. This unit wasn't as bad as I thought it would be because from last year's precal I had trouble with circular functions. Now, I understand how to figure out certain word problems and convert degrees into radians and vice versa. I also found that finding the sine, cosine, and tangent of angles are pretty easy and it's probably because of the mini quizzes we had. But finding cosecant, secant, and cotangent can be a bit confusing at times and may take up a bit of time for me to figure out. What helps me a lot is to look for patterns to solve different kinds of questions which makes it much easier to do.
On the other hand, considering the fact that I missed a couple classes last week, I was a bit confused with the graphing we had to do. At first I was like, "what is this?" But after a few explanations and practicing doing questions I got the hang of it. Remembering DABC actually helped me a lot to do the problems. Yet, I'm not totally comfortable with graphing because it probably takes me more time than others in the class.
In conclusion, this unit was "OK" and I hope I do well in the first test as well as everyone else. With that said, goodluck to everyone!
PS..were we taught the graph for tangent when I wasn't here? Because in excercise 6, I believe there is a question about it and I didn't know how to do it?! Help?
bob for Circular functions
Since our test is approaching for this unit I thought it was a good time to bob!
I was able to understand most things in this unit but my "muddiest point" would be the graphing part. I need still need some more practice with graphing those kinds of questions where all the DABC changes are there. I'm really comfortable with the A,B,C,D transformations but just not all together.
The part of this unit I really liked was probably those kinds of questions where you just have to find the exact values and simplify. At first that was kind of hard since we've all been accustomed to using degrees. I remember converting all the radians to degrees for each question, which was really time consuming. As I learned the exact values on the unit circle, I've found those kinds of questions way easier and didn't need to put it to degrees.
There's my bob for this unit. Good luck to everyone on the test this week?!
I was able to understand most things in this unit but my "muddiest point" would be the graphing part. I need still need some more practice with graphing those kinds of questions where all the DABC changes are there. I'm really comfortable with the A,B,C,D transformations but just not all together.
The part of this unit I really liked was probably those kinds of questions where you just have to find the exact values and simplify. At first that was kind of hard since we've all been accustomed to using degrees. I remember converting all the radians to degrees for each question, which was really time consuming. As I learned the exact values on the unit circle, I've found those kinds of questions way easier and didn't need to put it to degrees.
There's my bob for this unit. Good luck to everyone on the test this week?!
BOB.1 [Circular Functions]
Well now that I'm back from my Kenora basketball trip, and once again have computer access I thought it would be an oppourtune moment to do my BOB post for this unit. Alas, I find myself here doing exactly that. BOBbing!
Well I'll start with the bad, and work my way towards the good, seeing as how it also goes like that in terms of chronological order from the beginning of the unit to the end :)
The hardest part of this unit was definitely the very beginning. Now this had alot to do with the fact that I missed the first two days of class, having been sick with the flu (>_<). So by the time I had returned to the class on Wednesday (that being the third day of class) I had basically no idea of what was going on. However, with some help from my classmates, and a couple nights spent awake much later then I should have been, I managed to figure my way around the first couple days of work, and catch up to everyone else.
On the flip side, the easiest part of the unit, has probably been the memorization, of the patterns in the unit circle (which eventually lead to the memorization of the unit circles basic values for sine, cosine, tangent, etc.) I found this rather easy, because all I had to do, was draw the unit circle over the weekend, without referring to my notes. How simple is that? So after drawing the unit circle, probably 7 or 8 times over the weekend, taking about 3-5 mins each time (with that time frame getting smaller as I went along,) I managed to get a fairly good grasp of basic angles locations on the unit circle, and the trigonometric function values of those said angles.
Overall this unit wasn't very difficult to understand or grasp (at least for me.) I'd say the hardest parts of it all were related to the memorization of certain things (like what A,B,C,D mean in graphing f(x) = AsinB(x-C) + D). I also found it somewhat difficult at times to remember what to do when adding radicals or similar things that we learned in previous grades, and I haven't had to use in awhile. Besides that I found much of what we did within my abilities to understand and put to use in the exercises we've been assigned.
Well I think that about sums it up for this BOB. I hope everyone enjoyed their long weekend and I also hope everyone enjoys the rest of today :) I shall see everyone on Monday!
Ciao!
~Justus
Well I'll start with the bad, and work my way towards the good, seeing as how it also goes like that in terms of chronological order from the beginning of the unit to the end :)
The hardest part of this unit was definitely the very beginning. Now this had alot to do with the fact that I missed the first two days of class, having been sick with the flu (>_<). So by the time I had returned to the class on Wednesday (that being the third day of class) I had basically no idea of what was going on. However, with some help from my classmates, and a couple nights spent awake much later then I should have been, I managed to figure my way around the first couple days of work, and catch up to everyone else.
On the flip side, the easiest part of the unit, has probably been the memorization, of the patterns in the unit circle (which eventually lead to the memorization of the unit circles basic values for sine, cosine, tangent, etc.) I found this rather easy, because all I had to do, was draw the unit circle over the weekend, without referring to my notes. How simple is that? So after drawing the unit circle, probably 7 or 8 times over the weekend, taking about 3-5 mins each time (with that time frame getting smaller as I went along,) I managed to get a fairly good grasp of basic angles locations on the unit circle, and the trigonometric function values of those said angles.
Overall this unit wasn't very difficult to understand or grasp (at least for me.) I'd say the hardest parts of it all were related to the memorization of certain things (like what A,B,C,D mean in graphing f(x) = AsinB(x-C) + D). I also found it somewhat difficult at times to remember what to do when adding radicals or similar things that we learned in previous grades, and I haven't had to use in awhile. Besides that I found much of what we did within my abilities to understand and put to use in the exercises we've been assigned.
Well I think that about sums it up for this BOB. I hope everyone enjoyed their long weekend and I also hope everyone enjoys the rest of today :) I shall see everyone on Monday!
Ciao!
~Justus
Friday, February 22, 2008
BOB Version 1: Circular Functions
Nope, not done blogging for today. Just doing my BOB…
And so, Circular Functions, the unit, put a lot of emphasis on the unit circle. Memorizing (no, not memorize, but remember!) the values using mnemonics was the muddiest thing that I didn’t like about this unit. But remembering the unit circle did help me out as we progress through the course. Also just as equally as muddy was the group work assignment, The Unit Circle Triangle. I didn’t like that assignment ‘cause of its “challengingness.”
I remember in gr.11 we were studying how to graph trigonometric functions and Mr.K exposed us to the equation f(x) = AsinB(x-C) + D. He taught us what A, B, and D did to the sine graph but told us that we’ll learn what B does in gr.12 precal. Now, after over a year of waiting, I found out what B meant and that became my moment of clarity. B stretches/shrinks the graph horizontally.
I also liked how Mr.K did his 1st class on the 1st day of school because I remembered it as inspiring.
I also liked the helpful advice Mr.K said to one of his students: Remember folks, Mr.K says, “If you don’t memorized the unit circle, you will fail.”
By the way, does anyone know how to do Exercise 2 #15?
If f (x) = 2x + 3, find k so that f(k+2) = k + f(k).
Answer key says:
2(k+2) + 3 = k + 2k + 3
2k + 7 = 3k + 3
4 = k
...which doesn't make sense to me.
Also, one of our questions in our homework asked us to graph the tangent function. We weren't taught that.
And so, Circular Functions, the unit, put a lot of emphasis on the unit circle. Memorizing (no, not memorize, but remember!) the values using mnemonics was the muddiest thing that I didn’t like about this unit. But remembering the unit circle did help me out as we progress through the course. Also just as equally as muddy was the group work assignment, The Unit Circle Triangle. I didn’t like that assignment ‘cause of its “challengingness.”
I remember in gr.11 we were studying how to graph trigonometric functions and Mr.K exposed us to the equation f(x) = AsinB(x-C) + D. He taught us what A, B, and D did to the sine graph but told us that we’ll learn what B does in gr.12 precal. Now, after over a year of waiting, I found out what B meant and that became my moment of clarity. B stretches/shrinks the graph horizontally.
I also liked how Mr.K did his 1st class on the 1st day of school because I remembered it as inspiring.
I also liked the helpful advice Mr.K said to one of his students: Remember folks, Mr.K says, “If you don’t memorized the unit circle, you will fail.”
By the way, does anyone know how to do Exercise 2 #15?
If f (x) = 2x + 3, find k so that f(k+2) = k + f(k).
Answer key says:
2(k+2) + 3 = k + 2k + 3
2k + 7 = 3k + 3
4 = k
...which doesn't make sense to me.
Also, one of our questions in our homework asked us to graph the tangent function. We weren't taught that.
Wrapping Up and Concluding Circular Functions
3 assignments, 2 periods, 1 class. This is PC40SW08 (Pre-Calculus 40S Winter 2008).
As of now, Mr.K is still out-of-province because he was selected by The Council at the Conference last week to help write a textbook, but will return from his quest hopefully by Monday. And so, we had the same substitute as previous class'.
Period 1:
Our first assignment was Quiz 2 on Circular Functions in which we were not allowed to use our calculator. It was not a hand-in because the substitute says "according to the instructions Mr.K gave me, it did not say to hand anything in." So we assumed that we are not to hand that in. The class worked quietly during that quiz.
After finishing Quiz 2 on Circular Functions, we were assigned Graphing Trigonometric Functions. We were also told not to use a calculator when doing that assignment, but were allowed to use the calculator to check our answers. That is for homework, folks.
Period 5:
In our afternoon session, we were told to continue working on this morning's pre-calculus assignments and that Exercise 7: Translations #11-20 is also for homework.
HOMEWORK:
* Graphing Trigonometric Functions
* Exercise 7: Translations #11-20
* Circular Functions Test on Tuesday 26 or Wednesday 27
Next scribe is AnhThi.
That is all.
As of now, Mr.K is still out-of-province because he was selected by The Council at the Conference last week to help write a textbook, but will return from his quest hopefully by Monday. And so, we had the same substitute as previous class'.
Period 1:
Our first assignment was Quiz 2 on Circular Functions in which we were not allowed to use our calculator. It was not a hand-in because the substitute says "according to the instructions Mr.K gave me, it did not say to hand anything in." So we assumed that we are not to hand that in. The class worked quietly during that quiz.
After finishing Quiz 2 on Circular Functions, we were assigned Graphing Trigonometric Functions. We were also told not to use a calculator when doing that assignment, but were allowed to use the calculator to check our answers. That is for homework, folks.
Period 5:
In our afternoon session, we were told to continue working on this morning's pre-calculus assignments and that Exercise 7: Translations #11-20 is also for homework.
HOMEWORK:
* Graphing Trigonometric Functions
* Exercise 7: Translations #11-20
* Circular Functions Test on Tuesday 26 or Wednesday 27
Next scribe is AnhThi.
That is all.
Wednesday, February 20, 2008
Hey everybody, Paul here, doing my scribe post (since I got "voluntold" to). I hope 8pm isnt too late for a scribe post, but I guess you guys don't really need it all that soon anyway as we didn't do a lesson.
So yeah, today in Pre-Calculus 40S we had a substitute (Mr. Rekrus?), and he gave us an assignment per Kuropatwa's orders. The assignment was on circular functions and it went something like this:
You have a unit circle, and on this circle you have a point P, which is along the circumfrence of the circle and in Quadrant I. You also have point A, which is at the center of the circle (thus making it the origin), and a point B, which is positive along the X axis. If triangle APB is a right angle triangle, find the value of P that creates the largest area of the triangle.
Since this was a group assignment, the class was split into three groups. There was also supposed to be a time limit of 20 minutes, but the question utterly stumped the groups for most of the class, so the time limit was disregarded. Some groups finished the question before the end of class, some spent the entire class trying to solve it and some groups made little paper cranes.
And that was what we did today in Pre-Calculus.
Today's homework is Exercise 6, Questions 1-20. I suggest you atleast try them since we do have a test coming up.
As for the next scribe, I have chosen Zeph since he asked so nicely.
Good night and farewell.
So yeah, today in Pre-Calculus 40S we had a substitute (Mr. Rekrus?), and he gave us an assignment per Kuropatwa's orders. The assignment was on circular functions and it went something like this:
You have a unit circle, and on this circle you have a point P, which is along the circumfrence of the circle and in Quadrant I. You also have point A, which is at the center of the circle (thus making it the origin), and a point B, which is positive along the X axis. If triangle APB is a right angle triangle, find the value of P that creates the largest area of the triangle.
Since this was a group assignment, the class was split into three groups. There was also supposed to be a time limit of 20 minutes, but the question utterly stumped the groups for most of the class, so the time limit was disregarded. Some groups finished the question before the end of class, some spent the entire class trying to solve it and some groups made little paper cranes.
And that was what we did today in Pre-Calculus.
Today's homework is Exercise 6, Questions 1-20. I suggest you atleast try them since we do have a test coming up.
As for the next scribe, I have chosen Zeph since he asked so nicely.
Good night and farewell.
Tuesday, February 19, 2008
Graphing Sine and Cosine Functions
Hello, Francis here with your daily school scribe. Now I'll introduce you to the beginning of class. Let's bring it back.
Mr. Kuropatwa firstly showed us a new feature available on our blog. It's a translation feature that can translate this blog into one of many different languages. Brought to you by Google.
Mr. Kuropatwa also stated that the circular functions test will be sometime in the middle of next week. Which means that it would be a smart idea to start on your BOB posts.
Starting tomarrow there will be a substitute teacher and same goes for Thursday, because Mr. Kuropatwa won't be showing up for class on those days.
All of these functions that we graphed today are based on patterns and as said by Mr. Kuropatwa "Mathematics is the science of patterns". Okay now with today's lesson which was completely made up of graphing those sine and cosine functions, that are ever so interesting. As seen on slide 1 we started off class by graphing the sine function: y = sinx - 1 and on slide 2 the cosine function: y = 2cosx, then we stepped up to a slightly harder function found on slide 3 and I suggest you see how all that turned out, so check out that slide show. When graphing any of these functions you should remember a simple pattern: "1,2,3,4" where 1 is the maximum point, while 2 is the average point(between the max. and min. points) and 3 is the minimum point and 4 is the average once again. Remember when graphing one of these functions you should put arrows at the end, pointing in the direction the function is about to head to next, so if it's at the max point, and it has nowhere to go but down, you should end the line with an arrow pointing downward. Also remember not to put sharp points when you change direction from up to down or down to up, put curves, because if you put sharp peaks, then be prepared to lose your precious marks.
The general equation for these functions is: f(x) = Acos(x-C) + D or f(x) = Asin(x-C) + D.
When graphing these functions from these equations remember the word: DABC. This work or phrase is like the BEDMAS of graphing. It's the order in which you should always graph.
Now I will expose what these letters actually mean.
Firstly with D: is the vertical movement of the curve itself, it determines the sinusoidal axis(the axis between the max. points and min. points, its the average value of the curve.
Second is A: This is the amplitude it determines the max. and min. points of the curve on either side of the sinusoidal axis. The graph is stretched if the value of A is: |A| > 1 and its compressed if the value of A is: 0 < |A| < 1.
Third is B: this determines the period of the graph with an equation found on slide 18. If the value of B is negative then the graph curve will start with the pattern being 1,2,3,4. Where 1 is the min. point and 2 is the average point, and 3 is the max. point and lastly 4 being the average point.
Last is C: This shifts the curve left of right (horizontally). This is also called the "Phase Shift". If the value of C is negative(C <> 0) the curve shifts to the right.
For the sake of summarizing I will say this:
D - Lay down the sinusoidal axis.
A - Stretch of the amplitude.
B - Label the x-axis.
C - Look at the scale and slide the curve accordingly.
All of the details are found on slides 17-19. I suggest you check it out.
The sine and cosine curves are quite similar with the difference being that when at zero, cosine = 1 and sine = 0. But if the sine curve is slid to the right by pi/2, then at 0 sine = 1. With this, you can state that cosx = sin(x +(pi/2)) or sinx = cos(x-(pi/2)).
Well thats the 411 of today's class, hope it was helpful. The next helpful person to be voluntold(forced to do it for free, hence "volunteer that is told") is Paul.
That's me, the one and only, Francis! Until next time, I'm out.
Mr. Kuropatwa firstly showed us a new feature available on our blog. It's a translation feature that can translate this blog into one of many different languages. Brought to you by Google.
Mr. Kuropatwa also stated that the circular functions test will be sometime in the middle of next week. Which means that it would be a smart idea to start on your BOB posts.
Starting tomarrow there will be a substitute teacher and same goes for Thursday, because Mr. Kuropatwa won't be showing up for class on those days.
All of these functions that we graphed today are based on patterns and as said by Mr. Kuropatwa "Mathematics is the science of patterns". Okay now with today's lesson which was completely made up of graphing those sine and cosine functions, that are ever so interesting. As seen on slide 1 we started off class by graphing the sine function: y = sinx - 1 and on slide 2 the cosine function: y = 2cosx, then we stepped up to a slightly harder function found on slide 3 and I suggest you see how all that turned out, so check out that slide show. When graphing any of these functions you should remember a simple pattern: "1,2,3,4" where 1 is the maximum point, while 2 is the average point(between the max. and min. points) and 3 is the minimum point and 4 is the average once again. Remember when graphing one of these functions you should put arrows at the end, pointing in the direction the function is about to head to next, so if it's at the max point, and it has nowhere to go but down, you should end the line with an arrow pointing downward. Also remember not to put sharp points when you change direction from up to down or down to up, put curves, because if you put sharp peaks, then be prepared to lose your precious marks.
The general equation for these functions is: f(x) = Acos(x-C) + D or f(x) = Asin(x-C) + D.
When graphing these functions from these equations remember the word: DABC. This work or phrase is like the BEDMAS of graphing. It's the order in which you should always graph.
Now I will expose what these letters actually mean.
Firstly with D: is the vertical movement of the curve itself, it determines the sinusoidal axis(the axis between the max. points and min. points, its the average value of the curve.
Second is A: This is the amplitude it determines the max. and min. points of the curve on either side of the sinusoidal axis. The graph is stretched if the value of A is: |A| > 1 and its compressed if the value of A is: 0 < |A| < 1.
Third is B: this determines the period of the graph with an equation found on slide 18. If the value of B is negative then the graph curve will start with the pattern being 1,2,3,4. Where 1 is the min. point and 2 is the average point, and 3 is the max. point and lastly 4 being the average point.
Last is C: This shifts the curve left of right (horizontally). This is also called the "Phase Shift". If the value of C is negative(C <> 0) the curve shifts to the right.
For the sake of summarizing I will say this:
D - Lay down the sinusoidal axis.
A - Stretch of the amplitude.
B - Label the x-axis.
C - Look at the scale and slide the curve accordingly.
All of the details are found on slides 17-19. I suggest you check it out.
The sine and cosine curves are quite similar with the difference being that when at zero, cosine = 1 and sine = 0. But if the sine curve is slid to the right by pi/2, then at 0 sine = 1. With this, you can state that cosx = sin(x +(pi/2)) or sinx = cos(x-(pi/2)).
Well thats the 411 of today's class, hope it was helpful. The next helpful person to be voluntold(forced to do it for free, hence "volunteer that is told") is Paul.
That's me, the one and only, Francis! Until next time, I'm out.
BOB for Circular Functions
Hello everybody,
I believe the test on Circular Functions is this week so I decided to BOB ahead of time. This is our first unit of the course and I am doing great so far. The thing that really helped me in this unit is that activity that Mr.K got us to do and it was the one with drawing the unit circle and getting us to memorize those certain sine/cosine/tangent/cosecant/secant/cotangent of the special radian values. One thing I would like to do before the test is a little more practice. It should just give me a firm hold on the unit before the test.
Well that was my BOB and until our next text or my next scribe (which ever comes first) see ya and good luck on your tests.
I believe the test on Circular Functions is this week so I decided to BOB ahead of time. This is our first unit of the course and I am doing great so far. The thing that really helped me in this unit is that activity that Mr.K got us to do and it was the one with drawing the unit circle and getting us to memorize those certain sine/cosine/tangent/cosecant/secant/cotangent of the special radian values. One thing I would like to do before the test is a little more practice. It should just give me a firm hold on the unit before the test.
Well that was my BOB and until our next text or my next scribe (which ever comes first) see ya and good luck on your tests.
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