Bobbing!!!!!!

Hey everybody

Well i found this to be a pretty easy unit over all. The only part that I sometimes have trouble with is finding the "Good Idea" to verify the equations. That and making silly errors and just not catching them. The dance was hilarious and pretty weird but at least I can remember what to do with cos(x +y), cos(x-y), sin(x+y), and sin(x-y). Now it's just having more practice to making it even easier.

I can't believe the semester is pretty much HALF over!!! where did the time go?

Well anyways, see you guys in Precal and good luck on the test.

-Jessi

bob

hi every one, just doing my bob, --morning right before school..-- awtz

I found this unit interesting. there were some challenging parts, but the rest was pretty easy. I just lack of practice. I agree with them that you really have to practice to be good at something. I'm looking forward for the next unit, time for me to strive harder.

well.. good luck everyone for the test. enjoy!!

time to go to school =D

BOB

This Unit went by like rocket and now is coming to its end.
The most memorable thing about it was probably the dance that we learned while learning it. With more and more practice im sure everyone will do great on the test, who knows we might have to use the dance again later on.

Alright well then good luck guys on the test!

Time is going way to fast! Finally this unit has come to an end but I wasn't looking foward to it. I learned that the most important thing (well still learning) that you must do your homework! The best way to understand math is by actually doing it. You cannot teach something that you don't practise.

I found that this was the easiest unit to understand but unforunately I still lack practise. Just like everything else, there are different ways to achieve a goal although some ways are better than others.

Time to study!

BOB

Haha wow 3 units down! 4 more to go?

I found this unit, Identities, difficult. The problem for me is confusion I guess. The idea of remembering those *rules of thumb* was "eugh" for me, but if that's what it takes to successfully complete the test, then I don't mind (imprints it in his brain). Good thing Mr. K said that you have to do a lot of these questions to help you what ideas to use in certain scenarios. I hope I do well on the test, given that I'm not good at writing one.

Good luck everyone! READ OVER PJ'S "DOUBLE POST" BEFORE YOU GO TO SCHOOL! ahaha

BOB

Another unit has passed and another BOB and another helpful link are to be posted. IDENTITIES. All I can say is Mr. K was right. You really have to practice to be good at this. It's just a shame that I started practicing late. Doing the exercises gave me the confidence on solving Identities. There are a lot of things to remember when proving or solving them but I really feel good when I solve one correctly. :))

Hope everyone does well on the test! Good Luck!

BOB

Hey everybody, just doing my BOB. I found this unit challenging but not difficult. I liked how we had to "massage" the equation algebraically, it was like building a puzzle. I actually found it kind of fun!
The main thing you need to remember is the base ideas. The sin squared theta plus cos squared theta equals 1 and the cos(x+x) and sin(x+x). When you encounter an identity problem, just think "What is the clever idea behind this one? What identity should I use?". Once you are familiar with the bases all you have to do is use your standard knowledge of algebra, it is pretty straight forward.
So GOOD LUCK to all and I hope you all do WonderfullyExcelent on the test.

BOB

Hey y'all, it's your boy Kale here just gonna bob about out latest and dandiest unit yet, Identities. No, not the Bourne Identity, the math identity. This unit was about proving if one side was equal to another. I found this to be quite interesting because there are a massive amount of ways to solve them, there are so much ways to solve them that there isn't even a number, it's infinity! This is gonna be a difficult test, so brace yourselves! Good luck people!

BOB

Hi, here's my reflection for this Unit.

pro·cras·ti·nate (pr-krst-nt, pr-)

v. pro·cras·ti·nat·ed, pro·cras·ti·nat·ing, pro·cras·ti·nates

v.intr.

To put off doing something, especially out of habitual carelessness or laziness.

v.tr.

To postpone or delay needlessly.

I'll start off by saying that I knew just about nothing about this unit until I spent the last couple days working on it. I procrastinate, somehow thinking that I can put off doing any of the work until a couple days beforehand, just so I can have a little extra time. Well, it doesn't work. The point of those last statements is that I screwed up, and is mostly a public apology to myself for not trying and being lazy.Get in gear, jerk. =p

Anyways, I'm starting to find that this Unit is much easier then the previous ones. When I took the Pre-Test, I didn't understand anything at all, but now I'm beginning to understand.

This unit is very flexible. There are several different ways to achieve the answers for the most part and I like that.

Once we remember all the different identities, it's almost fun to try and plug them in to prove whatever is asked. I would cover all of them here, but since "renster" along with the others covered this so brilliantly, I would just sound like a broken record.

What really caught me off guard is the use of the Unit Circle. I didn't expect it would show up again, and I need to re-look over it to refresh my memory.

That's my reflection/BOB for this unit. Good luck on the test.

-ConstantEcho

BOB = BOB(backwards)

It's time for BOB again, this time it's on identities. Oh and lols to everyone who actually put "cleaver" instead of clever and I've seen many of them.

The first identities we learned about was the Pythagorean Identities.

The first one is that:

Then the next one is figured out by dividing everything by or .

If you divide by you get:

If you divide by you get:

Another identity type would be the even/odd identities.

Cosine is an Even Function, so cos(x) = cos(-x)

Sine is an Odd Function, so sin(x) = -sin(x)

Tangent is an Odd Function, so tan(x) = -tan(x)

The sums and difference identities has its own rap.

The rap for sin is "Sin, Sin, Cos, Cos, Sin.

The rap for cos is "Cos, Cos, Cos, BUST-A-MOVE, Sin, Sin

It goes Sin(a+b)=(sina)(cosb)+(cosa)(sinb)

It goes Cos(a+b)=(cosa)(cosb) - (sina)(sinb)

I think i have most of this stuff down, so I'm gonna go off to study and/or sleep (most likely sleep). Good Luck on the test tomorrow.

BOB

It's time for another BOB.
I think that this unit was easier than the earlier units that we've studied, and to be honest, I was doing fairly well. But then, Spring Break happened. Yes, spring break. Well, after the pre-test we had yesterday, I realized that I forgot most of the things we learned before the break. So I really have to study study study.

Here are a few things that we should know for the test.


PYTHAGOREAN IDENTITIES

EVEN/ODD IDENTITIES

SUM & DIFFERENCES IDENTITIES

DOUBLE ANGLE IDENTITIES

For this unit, unless the question is asking you to solve the problem, never ever put an equal sign. Use the "Great Wall of China" instead. That's why it is important to always read the questions carefully.
Mr. K gave us some strategies we could use to solve Identities in an elegant way, these strategies were:

• Work with the more complicated side of the identity first
• Rewrite both sides of the identity exclusively in terms of sine and cosine
• Use the Pythagorean Identity to make an appropriate substitution
• Simplify complex fractions, or rewrite fraction sums, or differences with a single denominator
• Use factoring (especially in difference of squares)
  

I really can't think of anything else to say, so I guess I'll end off this Bob post by saying, STUDY!

Good Luck!

BOB on Pythagorean Identities

Hello fellow classmates! Here's to the end of another eye-opening unit!
As routine procedure, here's a quick-fast BOB on Pythagorean Identities.
I feel like this will be bland compared to the BOBs already posted but I will contribute anyhow :]

Firstly, despite the test being on Thursday, April 09, 2009 we will not be having a review class tomorrow. That was today's class, which if I may add; was very helpful!
Tomorrow's class will be dedicated to starting a new unit so get ready guys!

Anyway! I'm going off on a tangent so I better get this done quickly...
There really isn't much to say so hmm...

• Well, I have to admit I totally abandoned the unit circle in my brain so I had to refresh my memory. Don't do what I did guys lol. Keep that unit circle in mint condition!
• Remember but do not memorize those corollaries! They will become extremely useful when proving identities.
  
• Keep the sine/cosine dance in mind, you'll never believe how it actually helps you out biiig time!
• As it occurred to me today, you may have to elaborate on both sides of the great wall in order to prove an identity. Astonishing, I know.
• Since we're on the subject, nothing ever crosses the great wall! Not even Q.E.D.
  
• Double identities may seem tricky, but really they're quite simple, just take your time.
  
• As usual, eat, sleep and study well!
  
• Practice, practice, practice! Unless you're confident enough already, that is.

I thought I had more in mind but I guess not. After today's pre-test, I feel like I need to review a bit more. I totally got pwned. However, that may be due to my lack of clever ideas. Oh me, why do I lack such useful mathematical creativity?

Good luck everyone :]

BOB

Okay, I do not know what to put in this BOB. All I have to say is this unit was interesting and momentous as it pertains to basic mathematics and somewhat advanced mathematics.

Ahh.. Well.. This is the third tribulation that has been casted upon us in our class. I suggest that you study if you are not confident. Just practice and practice. And to those who are confident, I suggest you study, or euphemistically REVIEW to increase the chances of attaining an honourable mark. I am fairly confident. I'll study tomorrow because my mind is currently devoid of focus and I don't want to harness any.

Hmmmmmmmmmmmmmmmmmmmmmmmm... I do not have any actual mathematical tips because everything that you need to know is in this blog and possibly your mind. It's up to you to make the effort to find the stuff. PJ has some good stuff I think. I just saw that his post was long haha. Interesting way to deduce..

What else.... Here's a brief characterization on the way I approach things. I'll try my best, which will most likely be not enough because describing the way the complex brain operates is difficult.

Read the question.
Interpret the given information, which can be direct but not always.
Make note of that information mentally, on paper, or whatever. Well, not necessarily make note, but if it helps then go for it, but I mean just know and understand what's given ha.
Attempt the question mentally and if you fail, too bad.
Try again with the same method or other methods.
Keep trying or skip.
If I get an answer, I take several other approaches to verify that my answer is possibly right.

Well, that looks like nonsense to me up there, but I'll leave it.

Good luck !

BOB = bob

This unit we focused on PROVING IDENTITIES. BOB = bob, get it? xD

Unlike what we did last unit, where we solved equations, here we proved each side to be equal. This meant that, the same expression looks different. Remember, we're not solving equations, we are proving them. (changing how they look). So never "cross the great wall of china"!

I was okay with this unit, nothing to complain about. But it would always take me awhile to see the "cleaver" CLEVER idea. This would be a problem when time plays a big role. (TEST) If you're going through the same situation as me, i suggest you do a lot of practice examples. There are links found on the blog to other references. AND Mr.K has left a bunch of practice on the previous slides. I'll be doing them tonight, so i'm down with comparing answers! :D

good luck on the test guys!
mary

BOB

Another BOB.
I find this unit not very hard, as Mr.K said if u find the cleaver idea than the whole thing will be easy.
I think I still needs some more parties on identities to get more better.
I think more time will help.
Hope I can do better on this unit and good luck everyone!!!!!!

Reflection on Identities

So... this one's going to be short and not very helpful to anyone. It'll just be a reflection on my part.

K, I didn't have a lot of fun proving the identities since the clever ideas never really got to me in time. XD They eventually clicked in my mind... after a while. That should still count for something, right? Hahah. I also keep forgetting the main corollaries even if there are only three of them. How sad.

The only break I got during this unit were the sum and difference identities. Yes, that would be the sine and cosine dance we performed during that one class. Hahah. Well, other than the dance I found that applying the sum and difference identities were manageable.

Meh, nonetheless I'll give it my best shot and study excessively until the day of the test which has been moved to Thursday. Good luck to everyone on the test!

By the way, lovely work on our mascot, Ingrid! :D She deserves brownie points for sure.

BOB

I found this unit quite challenging...Basically, this unit we learned about trig identities. The main thing we did in this unit was prove how two identities or expressions (or something) are equal. We learned that while proving that they were similar, we were not allowed to allow numbers, variables, etc. to cross over to the other side of the equal sign, or as Mr. K. says, the Great Wall of China. We were exposed to some other material such as how some identities are derived from cos^2 + sin^2 = 1. I understood how most of them worked, but i also had trouble understanding some of them. I think that was pretty much what we learned, and if it's not, then i guess you can tell that i still need a bit of help in this unit. Good Luck at the Test Everyone!

Identities for BOB

Hi BOB time again. This is gonna be quick and fast since I'm restricted to using a phone. Lets see, i really don't like this unit. Since it's all about the cleaver ideas and i'm not a clever person so therefore no cleaver ideas. But hope full i can get enough practice for the test.

TEST MOVED TO THURSDAY APRIL 9, 2009
But we are starting the new unit it tomorrow logarithms i believe.
don't forget to do your DELICIOUS bookmark. Know your trig identities.
This is taking me a very long time, well bye.
Good luck on the test.

-jennifer

pre-test day!!!

Hi everyone!

Today in math class we covered a lot and did some reviewing for our test on Thursday.

We started off with a pre-test! Here are the questions and answers.

Question 1

Simplify: sin(2x+π)

A) sin 2x B) cos 2x C) -sin 2x d) -cos 2x

Answer: C) -sin 2x
(highlight to see)

Here is the logic behind that idea....

sin(2x+π)= sina cosb + cosa sinb
= sin(2x)cos(π) + cos(2x)sin(π)
= sin(2x)(-1) + cos(2x)(0)
= -2 sinx

Question 2

The terminal arm of angle θ in standard position passes through point (m,n), where m>0, n>0. Determine the value of sin(π+θ).

A)

B)

C)

D)

Answer: A

Question 3


Question 4


Question 5

When we were done the pre-test we had time to do a quick review question.

Now for some final remarks about today's class.

1. thanks to Ingrid for making our awesome mascot!!!
2. check out the websites on the right hand side of the blog, for some extra math help. (www.math40s.com)
3. remember to give Rebecca a million dollars tomorrow!
4. There are some extra review questions on today's slides!
5. TEST ON THURSDAY! STUDY!
6. Don't forget to do your BOB
7. I just wanted to make 7 to finish the rainbow (:

The next scribe is my ANNABANANA!!!!