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Saturday, March 25, 2006

Jefferson's Scribe - Introduction to conics =3

YES I WAS CHOSEN TO BE FRIDAY'S SCRIBE BY NONE OTHER THAT MANNY!!! thanks pal. I don't know why but I'm really pumped on doing the scribe post. Alright its time to get to business shall we? Today was an interesting yet fun class today. we've met a new character in Mr K yesterday. Rurouni Sensei Kuropatwa was his name. (rorouni = wandering samurai. sensei = master/teacher in Japanese). He un sheathed his meter stick Katana blade(katana = Japanese sword) and asked the class what geometric shape it was. "Its a line Mr. K", says the class. And it was. Mr k grabbed his meter stick in the middle and started spinning it around really fast and then asked the class what shaped he was making. "Two cones Mr. K", says the class. And it was. He then took out his favourite cone (you know? the one that sits in the corner?). He then took his blade and sliced the top part off. It was so fast that the class couldn't see it. He then took off the top and told us that the cross view would be a circle. .He the cut the cone diagonally.(the slice was so fast that you couldn’t see it cutting through the cone). And out came a what looked like an oval or an ellipse. Then he cut it again at a steeper angle and out came a parabola. He then drew a diagram of a double napped cone and the cuts he made to it. Then he said that if you were to cut the cone perpendicular to it(vertically) it would make out a hyperbola. So a recap folks:

Circle- Starts a cone and made from a horizontal cut. At cross view it would be seen as a circle
Ellipse - found from cutting a cone in an angle. An ellipse is also a circle that someone sat on.
Parabola- cutting the base of the cone at a steep angle
Hyperbola - perpendicular to base
These are all called degenerates

Sensei K also said that a conic section has 4 ways of cutting. Those were the 4 ways I was mentioning about. He also said that if you also cut parallel to the vertex of the double napped cone it would be called a degenerate circle.(i'm not sure if that's what it's called)

We then had a new dictionary entry

Conics


There are 4 tipes of conic sections

1. Circles
2.Ellipses
3.porabola
4. Hyperbola


The conic section arise by slicing a double napped cone and looking at the cross section

The “Degenerates”: A point horizontal slice through the vertices produces a point, a degenerate circle. A line: A slice along one of the edges produces a line, a degenerate ellipse. A pair of intersecting lines a perpendicular slice through the vertices produces a pair of intersecting lines ; a degenerate hyperbola.
Locus: A fixed point used in generating the locus for a conic section

Directrix: A fixed line used in generating the locuz for a conic section

Locus definition for conic sections:
A locus (set of points) such that the distance from a fixed point(the focus) divided by the distance from a fixed line(the directrix) is constant.

The Circle:

Definition: The locus of points determined by a fixed distance(the radius) and a fixed point(the centre)

Deriving the standard form for the equation of a circle

(line)OP = T [by definition]
Sqr[(x - h)^2+(y - k)^2] = T [distance formula]
(x + h)^2+(y - k)^2 = T^2[square both sides]

The standard form for the equation of a circle.

Examples:

1. Write the equation of a circle with centre (-2, 3) and radius sqr(5)

(x - h)^2 + (y - k)^2 = y^2 h = -2 k = 3 r = sqr(5) (x - (-2))^2 + (y-(3))^2 = (sqr(5))^2 (x+2)^2 + (y- 3 )^2 = 5

2. Find the centre and radius of the circle (x - 3)^2 + (y - 5)^2 = 4

Centre (3, -5) Radius is sqr(4) = 2

3. Find the centre and radius of the circle x^2 + y^2 - 6x + 10y = 0


x^2 - 6x + y^2 + 10y = -9 x^2 - 6x +9 + y^2 +10 +25 = -9 +9 +25 (x-3)^2 + (y+5)^2 = 25
Centre(3, -5) Radius sqr(25)= 5

We also have homework:textbook, page 141 every 3 up to #63
And thus ends my scribe. I'M VERY PROUD OF MY WORK :")!!! well its time to pick monday's scribe 2 weeks from now. AND HIS NAME WILL BE CALVIN !!! Lets all give him a round of applause *applause*

And its time for me to leave. i've got a lot of things to do on my spring break list.

HAVE A NICE SPRING BREAK GUYS!!
YOU TOO MR. K!! =3



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A del.icio.us idea ...

We talked about this in class on Thursday. Students often find more, and better, sites than I do. You're better websurfers than I am. ;-) That got me thinking .....

I spend a lot of time looking for good websites that help us learn in this class. But what if we all spent a little time doing that? What if there was an easy way for us to both save our bookmarks (without cluttering up our favourites list) and share them with the whole class with the click of a single button? And what if we could access those bookmarks not just from home, but from any computer in the world? Hmmm .....

Well, there is an easy way to do that! Instead of saving bookmarks on your home computer sign up for a free account at a site called del.icio.us. You can then access them from any computer in the world. You can easily install a little button/bookmark that allows you to save any webpage you're looking at without interupting your surfing. Now we can all make recommendations to each other learning resources with the click of a single button in our del.icio.us accounts! Tag it using this tag:

pc40s

You should also tag each entry with several other words that indicate what it is about; things like: trig graphing stats circles etc. Also, include a brief descriptive clipping from the site (or type one in yourself).

As soon as someone starts saving links I'll add a del.icio.us box to the bottom of the sidebar of our blog. It will show the 10 most recently saved links automatically as you find them. There is will also be a link to the entire archive that you can browse at your leisure.

You can read this tutorial on how to get started with del.icio.us. You might also be interested in watching this screencast that illustrates just how powerful this web tool is.

Remember, this is part of your homework for Spring Break. You must save at least one link for each unit we have studied so far. Try not to post a link that someone else has already found. You can see what's already been posted by looking in our archive.



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Friday, March 24, 2006

Blog This, Blog That...

Okay, so it's test day today and I'm doing this right before I head off to school. Why? Simply because the truth is I am a procrastinator. I'm not entirely lost in class but if I just did the work I'd be fine. I realize that each time I do this, I basically say the same thing. I have the same problem to fix, yet I never do. I'll find a way before graduation, haha. Identities are a bit tough, but it just takes practice right? I have no problem remembering the Pythagorean Identities and the corroleries. Oh dear, I really should do my homework.



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Thursday, March 23, 2006

bloging b4 the test

we studied about identities and im really having a hard time with this unit. im really struggling doing an identities problem and im surprise to see how easy the solutions are after watching mr. k doing it on the board. knowing every identities formulas won't help you if you are not practicing using it to answer an identities question. im really disappointed at myself not being able to answer some questions about identities. i should try to substitute first the simpliest identities formulas before putting the complex formulas cause i often overlook those simple formulas that makes it harder for me to answer a problem.



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blogging on bloging

hey everyone, in this unit for identities was kind of easy but sometime I get confuse. Basically in this unit we have to solve equation, prove and find the exact value . I kind of understand except the double angle identities, and I have trouble with the proving. Today we did a review and it kind help me. I wish you all do best on test and have wonderful spring break.



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test time

The things that i had trouble in this unit is a applying the identities into solving problems. Also basically memorizing the unit cirlce values and appying them to solve equations, especially if the values go beyond 2 pi. Well this is all that I can think of, good luck on the everyone on the test.



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identities blogging on blogging

Todays class was very productive for me even though I had a mad headache that I had to struggled with while trying to concentrate. We did more practice on identities with previous exam questions. And it did really help me learn more about double identities since that section wasn't all clear to me. I guess I understand most of this unit, I understand the fundamental identities, the phythagorean identities, odd and even identities and the sum and difference identities. There is one thing though that I am still having trouble with and thats the trigonometry questions involving identities where your solving for x, the thing I'm having trouble with is when you must solve for csc x, sec x and cot x. I will try to clear that up before the test and I hope I wont have this headache tomorrow. Goodluck everyone.



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Trigonometric Identity Review / Scribe Post # 29

I so knew Regine was going to pick me (saw it in a dream). Well my computer is busted and so I'm using a friend's right now (yeaup that's how dedicated I am). Today's class was basically a review on Trigonometric Identities. The class was a big help considering the test is tommorrow and which by the way good luck on.

So, what we did in class was basically working on questions involving this unit. The questions are directly from the pre-calculus 2003 provincial exams, so expect similar ones like it.
The following questions we did were:

1) Solve for x on the interval [0, 2π]
3sin(2x) + cosx = 0
[ click here for answer ]

2) If secx = 3, find tanx
[ click here for answer ]

3) Find a root of f(x) = 2cosx-1
[ click here for answer ]

4) Simplify
(sinx + cosx)² - 1
[ click here for answer ]

5) Find the exact value of
cos(7π/12)cos(π/12) + sin(7π/12)sin(π/12)
[ click here for answer ]

6) Find the exact value of
a) cot(7π/6) - tan(π/6) - sec(π/6)
b) cos105°
[ click here for answer ]

7) Prove that
( cos²x / sinx - sin²x ) = 1 + cscx
[ click here for answer ]

And that's a wrap. We also did a few more questions on request, but they're similar to these. Good luck again on the test!

EDIT: Well my computer's fixed now =). And as you all may know I forgot to pick the scribe for next time, but I picked Jefferson in class. Just posting it for the record.



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bloggin on bloggin

Todays class was a good way to review the unit. Doing questions from previous provincial exams not only help us for the upcoming test, but also to see what kinds of questions they ask on the provincial exams. I am getting this stuff. Ever since we had that quiz on proving identities and looking at what teddie did, i began understanding it more. What I have to improve on is looking at a bigger picture and not being so narrow minded when trying to solve this types of questions. Identites and trigonometry are units that i enjoy working on.



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marcquin's blogging on blogging

Alright so I havent been to class lately due to some unfortunate events. I understand a little bit of the identities but for double identities I was not there to learn it. So my plan right now is to cram everything by this afternoon and hope for the best. All right guys after spring break i am going to work harder and harder until I reached the goal between 80-100.



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Wednesday, March 22, 2006

;testBLOG

identites, haha what an ugly topic. it was really confusing at first, but as time rolled and me hitting the books (literally) lol i began to understand. Like mr. k said, it's all about practice and nothing can happen if you don't haha and that's what i've been doing and i'm doing better but jsut having some problems understanding what the questions are asking me. just need to analyse more. also just need to work on remember those double identites. MR. K IF YOU HAVE A SECRET TO REMEMBERING THEM TELL ME NOW !! haha



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blllloogg

Well, since i've been absent for a couple of days, it's much more of a challenge getting all the stuff being taught. But when we go over it, it makes sense. double identities and that tangent thing, gotta work on that. And there are so many ways to solve identities, you get confused sometimes. Identities are hard..



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Blogging on Blog #3

For me this unit was going good at first when i got introduced to it. Than i found some difficulties because the equations were getting more complicated. When i look at the equation's i don't know how to start it and i think there should be more *Notes *and equations in class similar to the ones on our home work assignments.**The pre-Test really helped and i did the questions but only half the way. When i got to the group i was assigned i under stood the questions more because i asked for help and i got it.

***Well i wish every body good luck. The test is on Friday afternoon last day before Spring brake.=D



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my blogging on blogging mark.

hi precal 40s class, its me yet again.. i'm here to give my two-cents on this unit. im doing pretty good so far, i understand how the identies change from one another, the only thing i gotta do is make sure i remember all of the double angles and the other identities, after that is done, i should beable to do well on the test =D



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Teh BoB

BoB = Blogging on blogging.

Teh = Typo, oh so fun, maybe intentional?

Anyways, I'm just having trouble remembering all the identities, and that's about it.



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bloggin on bloggin :P

Today was the pre-test in trig identities. Overall it was pretty easy because im starting to get all this stuff. Like the sin/cos dance which is easy once you remember the formula. Solving these questions are like the block of wood Mr.K always refers to, there are many perspectives to these kind of problems but it depends on where you wanna go with it. But the thing that I still have troubles with is (like most of us) are solving certain identities such as the double angles or knowing when to use certain pythagorean identities. But like Mr.K said again its all about the practice. So thats all for now ladies and gents.



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Scribe 28.....

Today's class wasn't so bad. Thought it would have a lot of explaination on math, but it didn't!

Anyways, we started off the class with a pre-test. Quite a nice pre-test.


1) Simplify: sin(2x+ pi)

You have to use the "dance" or not! But you'll have a much more easier time remembering

Sin(2x+ pi) = (sin2x)(cos pi) + (cos2x)(sin pi)

Cos pi is -1. Sin pi is 0 which means (cos2x)(sin pi)=o. You're left with (sin2x)(-1) which equals to

(C) -sin2x



2)
The terminal arm of angle theta in standard position passes through point (m,n), where m>0, n>0. Determine the value of sin(pi + theta)

Since m and n are greater than 0, that must mean that the cooridinates are in Quadrant one. To figure out the third side, you use the pythagorean theorem.

You end up with: Square root of m^2 + n^2

sin(pi + theta)= (sin pi)(cos theta) + (cos pi)(sin theta)
= (0)(costheta) + (-1)(sintheta)
= -sintheta

Since n is sin, the result would be

-n/square root m^2 + n^2


3) In the triangle ABC, angle A and B are both acute. If cosA =1/2 and sin B=square root of three over two, then the value of cos(A-B) must be:

The easier way is to just use the pythagorean theorem to find the value. Either that or do it the long way. Take the exact values and plug it into the cos(a-b) formula. You guys know how to do this so I wont' show it.

(1/2)(1/2) + (root three/2)(root three/2)

1/4 + 3/4 = 1


Oh nevermind. It's better that you see the work. =)



4) Solve 2cos^2x + cosx - 1=0 algebraically x is greater than pi/2 and less than 3pi/2.

(2cosx-1)(cosx+1)=0

2cosx=1 cosx=-1
cosx=1/2

I didn't get to right down the right answers, so please tell me if these are wrong or not. These are my answers.

Answer: pi, 2pi/3, 4pi/3




5) Prove: sin2x/1 +cos2x = sec^2x-1/tanx

2sinxcosx/1 + cos^2x - sin^2x tan^2x/tanx
2sinxcosx/2cos^2x
(after all cancellations)

sinx/cosx

tanx tanx



That's what we did in the morning.




In the afternoon, Mr. K talked about this Delicious site. Well, it's not actually delicious. Well, if you think it is, what ever makes you happy works for me.

IMPORTANT: EVERYONE IN CLASS MUST SIGN UP FOR THIS BY TOMORROW

Create an account at this site- http://del.icio.us/
and install the button on your explorer. More preferably, you guys should use firefox because it's great and Mr. K said so. Listen to him. He's wise..
Also, Spring Break homework is to find a min. of one link for
-circular functions
-transformations
-identities

And post this onto your delicious account.


Then we had to solve these identities. We didn't have that much time to do them so I hope you guys understand this
.

sec^2x - secx=2

sec^2x- secx-2=0
(secx-2)(secx+1)=0
secx=2 secx=-1
cosx=1/2 cosx=-1

x= pi/3 +2kpi;kEI
x=5pi/3 + 2kpi;KEI



3sin^2theta-10sintheta-8=0

(3sintheta + 2)(sintheta -4)=0
3sintheta=-2 sintheta=4
sintheta=-2/3 undefined



cos^2x=sin^2x+sinx [0, 2pi]

1-sin^2 sin^x+sinx
0=2sin^2x+sinx-1


and from here, you have to use the quad. formula. Hopefully, Mr. K goes over this tomorrow too.

Anyways, that's it that's all.

Homework for you all: Page 278 from 27-49. All odd numbers.

THE SCRIBE FOR TOMORROW IS Jeffers---
MANNY!



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Sisyphus' Bloggon the Blog 3

So class today was kind of laid back for me, but I like to be laid back! We had a pre-test on the unit trignometric identities. I did fairly well on it on my own, but the discussion in our groups afterwards was a really big help! It was just too bad spy time wasn't of any aid this time, I guess our spy wasn't really spytatious (kidding Jefferson =P).

Anyway, during the unit, we learned that there are identities in identities that we could use it in other identities to solve for more identities. Yeah, in more understandable words, there are many many ways to solve it. It's best to preferbly solve it in a way, that all the math terms are alike (if majority is sine, then try to change the other terms into sine aswell if possible).

The most difficult thing for me in this unit, would have to be just knowing when to use an identity in another identity, and realising it. For example, realising that 2cos²θ-1 or 1-2sin²θ are the same and can be rewritten as cos(2θ). But now that I wrote it out in this blog, I think I could remember =)

So that's about it, good luck on friday!



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blogg on bloggingg

This blog is for the test on Friday, honestly when I see an identity, its like my mind goes blank. I don't know where to start and what to do. =s It's all very confusing, its almost like the identities are in a different language like what's going on!? Especially since there are no rules, it's even more difficult to try and solve identities. Today's pre-test really helped me understand identities a little more but I am still having problems with them.

Well good luck everyone, hope you all do well =)



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Blogging on Blogging

Since the test is on Friday so we have to do this again.This unit is pretty easy to me because this stuff is more on algebra which i like in Math. So yeah!! I like this unit I hope we all do good in the test. A tout à l'heure.



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Tuesday, March 21, 2006

Not really a scribe

Well, today was going to be my lucky day as a scribe. I was elated with joy and giddiness. Nothing could ruin the good mood filling my soul. It was as if the planets were patterned in some weird way that made life fair. But nooooooooooooo. I have to be scribe tomorrow. Two periods...AGAIN. Man, first time being scribe was heck. Oh well. Anyone relying on today's scribe got off lucky. YOU ALL DID. We did nothing today because there was a racial harmony event all afternoon. If you guys were there, you would have learned or re learned that racism is BAD.

I like Lavender.



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a blog on the blog

It's kind of early for this, i think. i will type this up now though, because i have the time to do this. well this unit started out okay. everything in the begining was confusingand i was LOST. I was confused on the very first topic, proving identities. Practise on that topic helped and most are fairly easy to do. I would have to say that i need more practise on the very current topic we have done in this unit. I think it is where we are given the sin or cos or tan of an angle and then we are required to solve for sin (A+B). These aren't too trouble some but i think with a little practise on these ill be ready for the test.



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BLAHGING ON BLAWGING!

Well its that time again where the class must post on the blog to get that one mark(very important) on the test. The unit we were working on (trig identities) is coming to an end as of Friday because we have a test(YAY!) I think that this unit was a pretty fast one, it only took about 1.5 weeks I think(?). Well enough about the class, more about ME!! Well, I'm progressing at a steady pace on this topic. I've understood the fundamental Identities and the odd and even identities. I still have a bit of trouble on the Pythagorean identities because I have difficulty on where to start. I know that I should start on the difficult side, but I'll get to a point where I cant go any farther and end up stuck. The sum and difference identities are what i understand(as long as they're in radians, otherwise i'm pretty much screwed in degrees) The sine,cosine dance really help me memorize the formulas. But i gotta remember the tan formula also.we've just learned the double angle Identities and I'm having a bit of trouble on that also. Overall I'm on a bumpy road on this topic but I am sure that I can smoothen things out with a lot of practice. I hope that Mr. K can give us some practice problems in class tomorrow as he does all the time :)

Well that's all for me HA, I'M THE FIRST ONE TO DO BLOGGING ON BLOGGING THAT MEANS EVERYONE ELSE WILL START DOING IT AS OF TONIGHT!!!

remember to study for your test guys, have fun

later days, Jefferson



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Monday, March 20, 2006

The 27th Scribe!!!!

Hey everyone! This is mike to the L. Haha. I would like to start this blog off by telling all of you to be careful what you wish for. Im saying this becuase I was begging Ahn to chose me for scribe for today's class. However i FORGOT that today was a TWO period math day. Hahaha. But anyways, it's all good!!
Today's class was another day of trigonometric identites. We started the day off by doing class problems. The first one is as follows:

1. If sinθ=3/5 and cosθ<0, Next we were to prove the following identites.
This is the end of the happenings of our first class! In the afternoon we wrote things into our dictionaries. What we wrote is as follows:
The following is a summary of trigonometric identities. This also goes into the dictionary for the people who missed today's class.
The last thing we did in the afternoon class was one more problem. The problem was as follws.

Finally i'm done!!!!!!!!!!!! Homework is on page 273 #25 - 40, every question including #43.

Hope that it made sense to the people who missed today's class and I hope you guys enjoyed this scribe post. Anyways the next scribe is ........REGINE. muahahahahaha!!!!!!!!!



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Sunday, March 19, 2006

Box Up Sunday!

This is a clever little game. You've got to get the small blue box inside the large red box. You can only push a box from the inside. The black boxes, if used cleverly, can help you get the blue box inside the red one. But sometimes they're just in the way. I made it to level 4 pretty quickly, but then it starts getting tough. How far can you go? ;-)

Have fun with this!




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Scribe number 26


Where to start on this scribe?...I'll start off by thanking Mark for this great opportunity...geeze. Haha I won't hold a grudge.
Well today's morning period 2 class started off with Mr. K. Talking about the coin hunt. The student coin was found by Emmedson Miranda at 3:34pm on Thursday, but all the math students already probably know that. My apologies for all the students he took advantage of haha. Anyways today we had quiz on trigonometric identities, which was out of a possible 12 marks. I found it quite difficult =/. Mr. K. Then went over the homework questions, it seemed like everyone was having problems with the degrees.
Math dictionary

IDENTITIES

I) The fundamental identities
1) Tanθ = sinθ/cosθ
2) Cscθ = 1/sinθ
3) Secθ = 1/cosθ
4) Cotθ = cosθ/sinθ

ii) The Pythagorean identities
sin²θ + cos²θ = 1
corrolories
sin²θ = 1 - cos²θ
cos²θ = 1 - sin²θ
tan²θ + 1 = sec²θ
corrolories
tan²θ = sec²θ - 1
1 = sec²θ - tan²θ
1 + cot²θ = csc²θ
corrolories
cot²θ = csc²θ - 1
1 = csc²θ - cot²θ

iii) Even and odd identities
cos(-x) = cosx [even]
sin(-x) = -sinx [odd]
tan(-x) = -tanx [odd]

STRATEGIES FOR SOLVING TRIG IDENTITIES

These are guidelines only. Nothing is eSometimesin stone. Somtimes you should NOT follow these guidelines. The only way to know when you should or shouldn't is by collecting experience by solving lots of identities.

1) Work with the "more complicated" side of the identity first.
2) Re-write both sides of the identity exclusively in sine and coPythagoreanse the pythagorean identities to make appropiate substitutions.
4) Combine fractions into a single fraction with one expression in the numerator and one in the denominator.
5) Using factoring in particular, keep an eye out for "difference of squares" type of factoring.

SUM AND DIFFERENCE IDENTITIES

sin(α+β) = sinαcosβ+cosαsinβ
sin(α-β) = sinαcosβ-cosαsinβ
cos(α+β) = cosαcosβ-sinαsinβ
cos(α-β) = cosαcosβ+sinαsinβ

example: find the exact value of sin(π/12)
since π/12 = π/3 - π/4
sin(π/12) = sin(π/3 - π/4)
sin(π/12) = sinπ/3cosπ/4 - cosπ/3sinπ/4
sinπ/12 = (√3/2)(√2/2 )- (1/2)(√2/2)
sinπ/12 = √6/4 - √2/4
sinπ/12 = (√6-√2)/4

PROOF OF THE SUM AND DIFFERENCE IDENTITIES

**{I had a picture for this section but it couldn't upload. =( I spent so much time on it too.}

√(sinα-sinβ)² = (cosα-cosβ)² = √(sin(α-β)-0)² + (cosα-β)-1)² [distance formula]
sin²α-2sinαsinβ+sin²β+cos²α-2cosαcosβ+cos²β=sin²(α-β)+cos²(α-β)-2cos(α-β)+1 [square both sides and expand]
1-2sinαsinβ+1-2cosαcosβ=1-2coPythagorean946;)+1 [using a pythagorean identity]
2-2sinαsinβ-2cosαcosβ)=2-2cos(α-β)
[simplify]
sinαsinβ+cosαcosβ=cos(α-β) [balancing and divide by -2]


YES, I'm done! SO happy, because I'm tiredI I have a stuffy nose, and i am frustrated.
CausetI'mribe is MICHAEL....cause i'm soo nice =D ahaha.



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Wednesday, March 15, 2006

25th SCRIBE

Hi everyone, today's scribe is MARK.
today was a 1 period class and we did some questions. =P

first we had a little more practise on identities.

1) sec x + csc x = (tan x + cot x)(cos x + sin x)

As we all know there are many ways to solve these problems. If you "correctly" worked one of the sides and then the other, you should have ended up with equal answers. One way to solve this problem is shown below:

Right Side of "="
[(sin x/cos x) + (cosx/sinx)][cos x + sin x] find the common denominator for the first part, inside the yellow brackets

[( sin2 x + cos2x)/(cos x)(sin x)][cos x + sin x] multiply the common denominator to the numerator and denominator, you get the values shown in this line. You may also combine the two with the same denominator.

[1/(cos x sin x )][cos x +sin x] sin2 x + cos2x is replaced by 1 because sin2 x + cos2x= 1. multiply.

[cos x/(cos x sin x)] + [sin x/(cos x sin x)] if you notice in this line we multiplied and seperate the one fraction into two. It is still the same value, but we have split them apart.

(1/ sin x) + (1/ cos x) we know that these are the reciprocal functions...

csc x + sec x so we can name them appropriately

2) (sec y -1)/(sin2y)= (sec2y)(1+ sec y)

For this question we can simplify both sides. It would would be best to start with the right side since it has secant and the left side is partly simplified. ut i will show how to do the left side, instead of the right =).

Left Side

(1 cos y -1)/(sin 2 y)

[(1/cos y) - (cos y/cos y)] / [sin2 y] turn everything into sine and cosine

[(1- cos y)/ cos y] . [1/sin2 y] 1 = cos y/ cos y

[(1-cos y)/cos y] . [1/(1-cos2 y)] multiply the first part of the expression by the reciprocal of the second(instead of dividing).

[(1-cos y)/cos y] . [1/((1- cos y)(cos y))] 1-cos2 y can e factored by the difference of squares

[(1-cos y)/cos y] . [1/(1+cos y)] final answer

you can use similar steps from this (left) side on the right side.

NEXT

Using these fractions or multiples of them (numerators only)

1/5, 1/4, 1/3, 1/2

find two who add or differnce is

a) 5/ 12 = (2/3) - (1/4)

b) 1/12 = (1/3) - (1/4)

c) 7/12 = (1/3) + (1/4)

d)11/ 12 = (5/4) - (1/3)

last thing of the day we learned some dance moves to an equation... it was fun and hilarious.

heres the song

sine sine cos cos sine

cos cos cos sign change sine sine

sine(alpha+ beta)= sine alpha cos beta + cos alpha sine beta

cos (alpha + beta) - cos alpha cos beta + sine alpha sine beta

We used these equations to solve one problem... I think the next scribe will post these equations ...so check out the next scribe post!!!.

hmm...Anh will be the next scribe =), YOu have three days =P...at least you don't have it on a week day =\








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Tuesday, March 14, 2006

Seek and ye shall find ...



The Coin Hunt has officially begun as of 12:30 this afternoon. The race is on! Who will be the first to find the coin? Will the students find their coin before the teachers find theirs? Who will win the pizza party? Which charity will benefit from this year's hunt?

Check the walls of the building as you walk into school in the morning for hints to figuring out the puzzles.

Happy π Day!!
Have fun with it. ;-)



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lucky scribe # 24

Happy π day and happy coin hunting everyone!

So today we had a two period day but it wasn't just an ordinary day. In our morning class we started off with two identity questions right away:



cos ø ∙ csc ø and sec² α-1


As we were doing these questions Mr. K give us a few sets of guidelines:
  1. start with the more complicated side, meaning the side with more variables
  2. rewrite everything with sin and cos
  3. always look fPythagoreanean related identities
  4. make a complicated equation simpler, not more complicated
  5. simplify as much as possible *e.g. compress different fractions into one fraction
  6. and you can always "rewind erase", make different choices nothing is engraved in stone.
*NOTE: These are not rules! There are no rules to solving identities! These are just guidelines!!!
And this is how one would solve these questions, but just remember that there are many many ways to solve identities.

cos ø ∙ sin ø
= (cos ø/1) ∙ (1/sin ø)
= (cos ø/sin ø)
= cot ø

sec² α -1
= (sec α -1) ∙ (sec α +1)
= ((1- cos α)/cos α) ∙ ((1+ cos α)/cos α)
= tan² α

So the rest of the period we were given more identity questions and did a lot of practice because that's the only way you'll get better on solving identities. In most of the questions given we had to use the Pythagorean identities. There are only three Pythagorean identities that you have to remember:


sin² ø + cos² ø = 1
1+ cot² ø = csc² ø
tan² ø +1 = sec² ø


Then from the three Pythagorean identities you can derive corollaries by balancing the equations.


For example from sin² ø + cos² ø = 1, you can derive two other identities:


sin² ø = 1- cos² ø and cos² ø = 1- sin² ø


Then in the afternoon class we celebrated π day!!! YEA!! Everyone brought pie, it was so awesome! We ate pie, LOTS and LOTS of pie with a good variety of flavors from apple, rhubarb, pumpkin, apple cranberry, blueberry, chocolate cream and coconut? cream? pie?!? Hmmmmm I probably ate 5-6 different slices of pie that were cut IN RADIANS.


Okay so we celebrated a little too early so at this point when everyone had their share of pie we did some math before π time. And in the spirit of π we did identity equations where 0 ≥ ø ≤ 2π we solved the equations graphically using our calcualtor and algebraically. Then we did a countdown 10 seconds before the official π time and on 1:59:26 everyone in class all together screamed "Pi!!!" while holding a piece of pie and stuffing it down our throats after. Ahhhhh π day... I'll miss you.



Thanks to everyone who brought pie, drinks, cutlery and anyone else who contributed to our π day celebration. Now do your homework, please.
pg. 264, odds, #'s 11-35
..and the next scribe is MARK.



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Monday, March 13, 2006

scribe # 23

Sup everyone Its Teddie again and today I'm doing my second scribe of the year. This week is going to be a good one with pi day and everything tomorrow. Well anyway lets get to the stuff we did today. Today was a 1 period so we start off in the afternoon. We go straight to the math dictionary: We continue to draw and put properties for the "other" trig functions. (Excluding sin and cos ). We finished writing down the stuff for tangent and cosecant.


THE SEACANT FUNCTION

secx = 1/cosx


Properties of the SEACANT function

Domain: { x x =/= pi/2 + k(pi); k E I, x E R}
Range: (-infinity, -1] U [1, infinity)
Amplitude: undefined
Period: 2pi
Roots: none
Y-intercept: y = 1
Symetry: even function
Asymptotes: pi/2 + k(pi); k E I


THE COTANGENT FUNCTION

cotx = 1/tanx or sinx/cosx


Properties of the COSEACANT Function

Domain: { x x +=/= k(pi); k E I, x E R}
Range: (-infinity, infinity)
Amplitude: undefined
Period: pi
Roots: pi/2 + k(pi); k E I
Y-intercept: none
Symetry: odd function
Asymptotes: k(pi); k E I

And thats all for our math dictionary today.
Now on to the stuff we learned:

In the diagram above is a right angle triangle with its hypotenuese congruent to the radius of the unit circle. Considering that we know what the value of the angle x, and that the hypotenuese is 1 (radius of unit circle). Finding the opposite side would be opposite/hypotenuese or sinx. Find the adjacent side would be adjacent/hypotenuese.

Considering the pythagrium theorum, (a^2 + b^2 = c^2)

this equation would be true

sin^2x + cos^2x = 1

Then we went over some questions

Solving Trig Identities (we first simplify and find a common graph)

(secx)(cotx)
=(1/cosx)(cosx/sinx)
=1/sinx
=cscx

To do this vice versa

cscx
=(1/sinx)(cosx/cosx) <-- multiply by 1 =(cosx/sinx)(1/cosx) =(cotx)(secx)

2 guidelines to consider:

1. rewrite the whole thing using sin and/or cos
2. work with complicated side 1st reduce and substitute as much as you can

Well thats all folks, and tomorrows lucky scribe is...............JANET!








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Sunday, March 12, 2006

Sunday Knight



How far can you go? Play here! ;-)



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Saturday, March 11, 2006

Scribe #22

Hey guyzzz.... It's me again, Emile your scribe for Friday, March 10,'06. The first part of the class in the morning, we had a debate about what time would be the test? The majority decided that we held the test in the afternoon.

After the class debate, Mr. K asked us, if we have any question involving any topic in transformation and word problems. Some of our classmates asked about the even and odd functions. Here are some examples:

An example of even function:

f(-x)= f(x)

f(x)= 2x2-4

f(-x)= 2(-x)2-4
f(-x)= 2x2-4; It is an even function because f(-x)=f(x).


An example of an odd function:

f(-x)= -f(x)

f(-x)= (-x)3-(-x)
f(-x)= -x3+x

-f(x)= -(x3-x)
-f(x)= -x3+x; In this case it is an odd function because f(-x)= -f(x).


Another issue was brought in and it was the reciprocal function or 1/f(x). And it was like this:

f(x)= 2x2-4
















Then half part of morning of the class we wrote something in our Math Dictionary about:



The other Trig Functions


The Tangent Function

f(x)= tanx
















Properties of the Tangent functions

Domain:{xlx is not equal pi/2+kpi; k is an element of I, x is and element of R}
Range: (-00,00) or {yly is an element of R}
Amplitude: undefined
Period: pi
Roots: kpi ; k is an element of I



The Cosecant Function


f(x)=cscx= 1/sinx















Properties of the cosecant function:

Domain: { xlx not equal k pi; kis an elemnt of I, x is an element of R}
Range: (-00,-1] U [1,00)
Amplitude:undefined
Period: 2pi
Roots: none
y-intercept: none
Symmetry: an odd function


That's all for me now. Oops! before I forget the next scribe is Teddie. A tout à l'heure.



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Friday, March 10, 2006

Test Blog

I honestly forgot that we had to do this, that's why this is very last minute. That, and I don't want to have to lose out on a mark on the test. So class? For me, what we learned was going at a fast pace for me. Understanding the material was quite a challenge for me, but because we did a bit of review this morning and the pre-test yesterday, certain things seem a little less complicated. One thing I found was a challenge was the word problems that were given to us. I'm at a level of comfort that I will approach completing the question without fear, but I seem to underestimate myself.

Other than my minor struggles, class has been going well. The students and Mr. K (you guys) are always a pleasant bunch to be around.



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blogging for the test

Well I guess some of the things that I had troubled in this unit would probably be yes! the word problems, but also understanding even and odd functions. I just dont understand how you would find if it's an ever or odd function algebraically. I guess the biggest problem that I have with the word problems would be finding the period and using the information to actually draw the graph. Well I guess that's about it. Good luck everyone!



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Scribe # 21

Sorry for the late scribe, I had work until 10. Okay well in class today we did another pre-test for the test tomorrow. It took the whole class, so that's all we did. The pre-test consisted of 5 questions.

The first two questions were multiple choice.

1) If f(x) = 2x2 - 3, where x is less then or equal to 0, then a function g that will have domain and range that are both different from those of f is:

a. g(x) = f(-x)
b. g(x) = -f(x)
c. g(x) = f-1(x)
d. g(x) = k f(x), k > 0

The answer for the first one was C. I'm not really sure why that's the answer, so if anyone can help me out on that one, it would be greatly appreciated.

2) The graph of a function f is a parabola opening upward, with it's vetex on the x-axis. The graph of a new function g, where g(x) = 2f(x), will have

a. the same domain and the same range as f
b. the same domain but a different range than f
c. a different domain but the same range as f
d. a different domain and a different range than f

Here's a diagram to help you understand this more:

So the answer for question 2 is A.

3) Given the graph f(x) below, sketch 1/f(x)




5)This water wheel rotates at a rate of 5 revolutions every 4 minutes. Its bottom edge touches the surface of the water.

a.The point A is on the wheel. Sketch a grpah ofthe height of the point A above the outflow water level as a function of time, starting at t = 0 seconds, with A as shown.



b) Write a sine and cosine equation for this function.

Sine Cosine
A= 5 A= -5
B=2pi/48 B= 2pi/ 48
C=12 C= 0
D=5 D= 5

h(t)= 5 sin [2pi/48 (t-12)] + 5
h(t)= -5cos [2pi/48 t ]+ 5

c) Find one time when the point A is 4 meters above the water.

4= -5cos [2pi/48 t ] + 5
-1= -5cos [2pi/48 t ]
1/5 = cos [2pi/48 t]
1.3694 = 2pi/48 t
10.4617 = t

d) For how long, during the revolution, is the point A within 4 meters of the water's surface?

By symmetry, A is within 4 meters of the water's surface for 2(10.4617) = 20.9235 seconds each revolution.

Well its almost 1 now, but I'm finally done. YAY! Sorry if everything seemed kind of rushed I'm just really tired now and I want to go to sleep. Oh yeah still waiting for help on question 1.

Anyways the next sribe is Emile.



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Thursday, March 09, 2006

bloggin on bloggin

I'm thinking that this unit went a lil bit too fast. And it seems easy but little things can mess u up. Like long answer questions is all about the graph, if u mess up the graph the whole question is goin to be wrong. The assignment Mr. K gave on the board last time, messed me up big time just because I started off at 0 instead of 5. Then I wrote the wrong equations for (b) and did not find the right answers for (c) and (d). My advice to u guys is be careful.

have fun on the test tomorrow.



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bloggin on blog Zaenab

I thought that this unit translations it will be easy and finally i am getting prec40s but when mr.k introduced us to the word problems i was lost again and confused. The next day we had more problem solving questions on the borad and i know what i was doing in class because i got some explinaton from my friends but when i came home i couldnt do them i tried to look back at the examples i did in class and refresh my mind but i still couldn't get the word problems and that is my weekness. Therefore i was stuck on the word problems.

Zaenab



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The Mystery Coin Hunt!

π Day is around the corner .. it's five days away! Soon, soon, the hunt will be on!




Somewhere on the property of DMCI a coin will be hidden. Hidden so carefully and cleverly that it cannot be discovered by chance or simply by looking for it. On March 14, π Day, the coin's location will be revealed buried in a series of riddles and puzzles. Until it is discovered the coin's location will remain a mystery....





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Wednesday, March 08, 2006

bloggin on bloggin

This unit is going by easily for me. The hard thing about the unit transformations are the problem solving. My weaknesses in math are problem solving because I have trouble applying the work that we have learned into the problem. I guess better practice and trying to see things from different perspectives will help and improve my work. Another thing that I found hard was the question today on the quiz. We were asked to express the following equations when given a graph to look at: g(x) as a function of f(x) and F(x) as a function of g(x). This was just something new a confused me with the wording of the question. Overall I like this unit but I can still improve by a whole lot.

MikeL



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Hi i am zaenab




scribe for today. The 1 class in precal started by Mr.K giving us a word problem on the bored and with it came some questions as usual.


igh tide at the port of montrial occurs at noon today, the depth of the water will be 15m, at low tide. The depth will be 6m, low tide will occurat 6:12 pm.

a) Sketh the graph for this function.
b) Write 2 different equations for this graph. One sine and one cosine.
c) The best time to go fishing off the pier is at 5:18 pm. How deep will the water be?
d) A ship needs a minimum depth of 12m to get into port. What is the maximum amount of time the ship can safely stay in the port?


Answers:

a)graph @ the bottom (soory i couldn't leave it at the top)

b) sin cos d(t)=-4.5sin[2 pi/12.4(t-3.1)]+10.5

A=-4.5 A=4.5 d(t)=4.5cos[2pi/12.4(t)]=10.5

B=2pie/12.4 B=2pie/12.4

C=3.1 C=0

D=10.5 D=10.5

We get A 15-10.5=4.5 for sin it is negative because the graph goes down and it should go up.

We get B 2pie/B B=12.4 the period which is shown on the graph.

we get c by looking at the graph therfore we see the graph first starts at 0 that is for cosine for sine the graph starts at 3.1.

We all can find D it must be an easy mark for all of us. D is looking at the period and seeing where the sinasoidal axis is in the middle in this case it is 10.5.

c) We are aske how deep will the water be at 5:18 pm and :18 is 1/4 of an hour (i think sorry if i am wrong and please tell me the writr answer) So we convert :18 to hours and that is 0.3. We did that by 18/60=0.3

We will just substitute the new t 5.3 to any of the equations.

We used the second one

12=4.5cos[2pi/12.4(t)+10.5

than 12-10.5=1.5

1.5=cos[2pi/12.4(t)]+10.5

1.5/4.5= cos [2pi/12.4(t)]

1/3=cos(12.4/2pi)2pi/12.4=1.2310(12.4/(2pi))

t=2.4293

d)the answer will be in Quad 1 or 4 because cos is positive.

In period 4 we thought we were going to do a pre test but we did a Quiz some people were strugling with the 2 question but than when mr k explained it it became clear. The first question was clear and easy i hope every body got the two marks it was wirth.=)

1) Given the gragh of f(x), sketch the graph of f(x+1)+3.

this is telling us to go 1unit to the left and 3 units to the left.

The graph for #2 is in blue and red.

2)iven the graph of f(x)and g(x):(4marks)

(a) Express f(x) as a function of g(x)

answer; f(x)=g(2x)

(b) express g(x)as a function of f(x)

answer: g(x)=f(x/2)

3) Given the graph of f(x), sketch the graph of f-19X0on the same cartesian plane.(2marks)(The graph will be colored in red look for it at the bottom)

4) State whether of the following is even, odd or nither.(4 marks)

a)f(x)=3x2 Even

b)f(x)=-sin(x) odd

c)f(x)=3x Even

d)f(x)=-4x2+3x Neither

you could check your answer by the following equation.

f(-x)=f(x)

f(-x)=-f(x)

Jacky is the next sckribe=)
have fun jacky



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Tuesday, March 07, 2006

Test Blog

Translations seems to be pretty simple. It's just about remember each little thing effects f(x) so easy enough. Then got hit with word problems =/. this is probably the hardest thing i've seen in my life. Why ? Because it's just not clicking in my head. Like I understand everything and anything when Mr. K explains it in class and i'm understanding. Home comes and I look at my notebook with a blank expression on my face. Yeah it's troubling me that much. This is probably the only thing troubling, I guess I need someone to explain it in the simplest way possible.



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hi guys, my name is senait and I am today scribe. Today pre cal class was in the afternoon during period 4 and it was kind of quite class because we had review yesterday on transformation and the word problem was difficult to solve. The review was
2 The depth of water in a harbour can be approximated by the equation: d(t)= -3.5cos0.17pi t+12 where d(t) is the depth in meters, and t is the time, in hours, after low tide.
(a) graph the function without using your calculator?
(b) what is the period of the function? What does it tell you about the tide?
(c) an ocean liner needs a minimum of 13m of water to dock safely. For how many hours per cycle can the ocean liner dock safely?

(b) P=2pi/B

=2pi/0.17

=1.76

(c) 13= -3.5cos0.17pi t+12

1= -3.5cos(0.17pi t)

1/-3.5=cos(0.17pi t) we can think as sta

0.17pi t/0.17pi = 1.8605/0.17pi

t= 3.48

pi-1.8605 to get alfa

alfa=1.2816

pi-alfa= 4.4227

0.17pi t/0.17pi = 4.4227/0.17pi

t = 8.2811

To find hours : 8.2811-3.48= 4.797

4.797-4 = 0.797

0.797*60 = 47.82

3. The average daily maximum temperature in Victoria B.C reaches a high of 23 C on July27, and a low of 5 dgreeC on January 5.

(a) Model this situation using a sine and a cosine function.

(b) Graph the function without using your calculator.

(c) How many days will have an expected maximum of 20 degrees or higher?

July 27, max 23 degrees

January 5, min 5 degrees

Jan/31, Feb/28, Mar/31, Apr/30, May/31, June/30, July/27 =208

period=406

T(d)= 9sin[2pi/406(t-106.5)]+14

T(d)= -9sin[2pi/406(t-5)]+14

the next scribe id Zaenab.




















































































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blog b4 d test

Well tomorrow is our pre-test & the next day is our test. The word problem solvingthat Mr. K did on the board today seems easy when i'm just listening & seeing what he was doing but when I'm trying to solve the problem by myself, I'm usually having trouble and don't know what to do. I still need some practice on that part. The transformation lesson is not that hard & I'm having fun doing it. I really like this unit. I just hope I can do well in those word problem so that I can participate well in the group discussion in tomorrow's pre-test cause I wasn't able to help my group in the last pre-test.



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blogging again blogging

Well i think this unit was fairly easy... but i still had moments of confusion. Reflections over the equation y= x was hard to do. Everything else like translations and reflections i was ok with. I would have to say the most difficult was the word problems. Y ou have to work with a small bit of information and expand, to answer the questions. Today's class helped a lot on understanding how to do some word prolems. I think if i practise i think the word prolems on the test will be a snap. Well that's all i have to say for this unit.

MC



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Monday, March 06, 2006

blogging on bloggger

well lets see, when i can teach some one how to do the stuff, it makes me feel really good and confident that i can do well in this course. just the homework slacking problem is going to catch up to me.. haha but i really think i've this stuff down =D just gotta do some of them relating trigg graphs to real life situations to make sure i can do it easy.



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blogging post on translations

Today Mr. K was away for the whole day so we had a substitute. We worked on the review worksheets that were given to us for both classes. Today the substitute made the funniest comment. He was always encouraging us to talk amoungst each other but we didn't know why and finally he said "You guys are too quiet and too focused, please talk to each other." Well I thought it was funny.

Translations started out as an easy unit for me. Everything was easily understantable, I'm confident that I know how to do all the translations in an equation, then graph it and how to derive an equation from a translated graph. Basically I understand everything up to the word problems. I think most people are having trouble with the word problems, it's really hard to relate math to real life problems. I just hope that I can have that "moment of clarity" soon before the test...



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Sisyphus' Bloggon the Blog 2

So, in todays class Mr.K wasn't present, and so there was a substitute. It was sort of a relaxing class, which I liked, because yeah... I loove to relax! But anyway, we worked on two reviews on transformations, which is our unit we are currently studying on. I think I'm doing fairly well upon the topic, I understand most of it.

The problem for me, which I found out today, lies within the word problems. In the review there was this one question that practically stumped everyone, without the use of actually graphing it on a calculator and doing it by ourselves ( letter c in question number 2 to be more specific =D ). And for the other word problem, the answers can vary, depending on how you graph it, so I don't know if I'm doing it right =S, and also letter c for that question bugs me aswell.

A Topic Totally Unrelated to Math (don't have to read) -

For the game gridlock, which was our Sunday game Mr.K posted up. I've made it to level 28! Sorry Mark =P. I did it within an hour, and I had to stop because of work =(, but then later finding out I wasn't working after I arrived. I was too disappointed to start all over because I shutted my computer off (So much for sisyphus hey? I bet even he takes some breaks though =P, and that's what im doing). I'm just bound to bad luck it seems.

Oh, and my random act of kindness today, was pushing a helpless lady's car stuck in the snow when I was walking home afterschool. What are the odds of someone who went out to buy kitty litter earlier in the day get stuck in the snow. Yep, my incredible idea was to use it for traction. It was a success! But while I pushed the car out with my girlfriend helping, I was smoked with kitty litter mixed with snow all over me by the rapid spin of the tire. Yeah, just another example of bad luck for today. And to top that off I dropped my supper on my shirt, twice, once the whole plate, and the second time about half of it. Don't ask me how. Well, I'm not trying to be pessimistic, I'll just think of it as, it could always get worse.

EDIT:


Yeah, so for the gridlock game, I've done it! Took me awhile (about 2 hours, a little less). These math games always keep me from doing my homework. SISYPHUS!



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blogg on blogging

In this unit it was kind of hard, because when the graph was compression, expansion, reflection and translation. I understand the reflection and compression but I am having trouble with the expansion, translation and stretch.
Also I have difficult drawing with,
y=(1/x+3)+5
Hopefully, I will know what I going to have more difficult with this unit, when I take the pretest.



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Sunday, March 05, 2006

blogg on bloggingg

Transformations, what can I say, I am confused. There's too much going on all at once and there are so many different graphs. It's not like doing just parabolas or sine and cosine functions. It's a whole bunch of different graphs. I don't know if I can correctly draw transformation graphs or write equations for them and the test is so soon too. Stretching, reflecting and translating, its too much for me.

*deep breath..I'll read my math dictionary repeatedly and hopefully I'll start to understand whats going on.



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Blogging on Blogging

As this unit comes to an end, the thing that I just find it hard, well not hard... sort of hard was doing the expansion and compression, although Alridge taught me some of it, I sort of get it now. But when the expansion or compression, reflection and translation are all in one equation I just don't get it from that time on...
All in all this unit is lot easier than the last unit that we had... A tout à l'heure and Au revoir



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Sunday Gridlock...CHAMPIONS?

well i decided to make this post for fun =). i tried the gridlock game and got to lvl 25 woot woot. Any1 else who tried gridlock post what lvl you got up to =)




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blogger blogging on blogging blog blog

Well, I'm having trouble with where you should draw the reciprocal of a function. Not all of them. This particular example.

Draw the reciprocal of f(x)=3x+5

And what I'm getting is not what my CALCULATOR is getting. But I'm smarter than my calculator right? Probably not but I made myself feel better. This unit wasn't so bad. Hopefully, the next unit is a bit more fun than this one. Can't wait until pie day...



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Don't laugh it's my first time

This is my first time making this so don't complain because I don't complain when you made yours hahaha...ok and if something goes wrong I don't want to hear it in class aight.


Trigonometric modeling
For Saskatchewan town, the latest sunrise is on December 21 at 9:15 AM. THe earliest sunrise is on June 21 at 3:15 AM. Sunrise times on other dates can be predicted from a sinusoidal equation
NOTE : there is no day light savings time in saskatchewan.
A) sketch a graph of sunrise times over the year
B)write 2 equations, one sine and one cosine to describe sunrise times over the year.
C)use the equation to predict the time of sunrise on April 6.
D)on what dates will the sun use at 7:00 am?
A)
Find the D-coordinates for June 21
  • number the days between the max and the min
  • on the graph june 21 is day 172 since half the period is 182, the full period is 2(182)=364 days
  • Also 1/4 of the period is 182/2= 91 days

B)
Sine
A=-3
B-2pi/364
C=81
D=6.25 s(d)=-3sin 2pi/364(d-81)6.25
Cosine
A=-3
B-2pi/364
C=-10
D=6.25 s(d)=3cos 2pi/364(d+10)6.25
Find D for April 6
C)
month / #days
jan 31
Feb 28
Mar 31
Apr 6
Total 96
s(96)=-3sin[2pi/364(96-81)]+6.25
=5.48188 - 5 X 60
5:28 .9130 - 28 X 60
5:28:55
for COSINE fill in just like SINE well not exactly like it because they have diffirent ABCD's well you know what I mean, I didn't do it because I was lazy and stuff so yea...Ah whatever I'll do it any ways
s(96)=3cos[2pi/364(96-81)]+6.25
=5.48188
5:28 .9169 - 28 X 60
5:28:55
D) s(d)=7
7=-3sin[2pi/364(d-81)]+6.25
for now "@" will represent theda since I don't know how to make theda and plus I don't know how to spell theda so if your getting angry or something about it don't, cuz I didn't bother to learn how to spell it, if it is wrong tell me in class and don't laugh cuz I cry easily...
let @=[2pi/364(d-81)]
7= -3sin@ +6.25
.75=-3sin@
-.25=sin@
@=-.2526
now the last part I can't make out cuz I think I was writing sloppy so I went to calvin and got his notes to see what the last part was and I got home and I realized that calvin's writing is not as adaquite basically his writing really sucks sorry man I'm just saying and sorry for typing it down and telling everyone that your writing is terrible...we still cool "G" ? aight cool...
I'll try to do this last part from both notes but If it's wrong I'm sorry
(364/2pi) 2pi/364(d-81)=.2526(364/2pi)
d=.2526(364/2pi)+81
d=66.3662
d=66 or march 7
ok That's it if there's anything wrong with it like if you can't see the graph or something that means your eyes are closed hahaha just joking but seriously your eyes are closed...don't tell me if it was to hard to see cuz honestly I can't see it either...and the scribe...will be randomly selected...I will close my eyes and who ever hasn't been a scribe yet must stand in a circle around me and I will point in any random direction, if I point in your direction you will be the scribe, I'm only doing this cuz I can't decide and wanted to do something diffirent with choosing the scribe...



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BLAHGING ON BLAHGING

well this new unit was quite interesting, although its all graphs i find this a little easier than the last unit a bit. honestly i don'n know what i have trouble with, but i know i do have trouble in some other the things we working on. i understand the reciprocals and inverses(i think) and the translations and the compression and stretch(i'm still not clear with which is a stretch or a compression). Anything that i havent mentioned might be the ones i have difficult with. I'll know what i have trouble with as soon as i take the pretest.
later days, LAWL



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Sunday Gridlock



In this game you have to move the blocks (vertical blocks move only vertically and horizontal blocks move only horizontally) out of the way so that the blue block can slide out the "door" on the right. Although this game can sometimes get frustrating there is always a way out. Remember Sisyphus!

So far I've made it to level 6, how far can you get?



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Friday, March 03, 2006

It's Coming ...



π
Watch it grow.



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Thursday, March 02, 2006

lucky scribe!!

Well today is a two period pre-cal class. On our 2nd period class, Mr. K isn't around cause he's sick (get well soon Mr.K) so we have a substitute teacher, Mr Fallorin. We were told to finish doing our yesterday's assignment which is the chapter review, every 2nd question up to number 44 pages 64-65. On our 4th period class, classes starts at 1:45 because there is a film viewing at the gymn (they watch the dodgeball movie). Some came to class late because the movie. We continue doing the assignment. That's everything we had done today. A very short scribe for today!

the next scibe is ....................... lerwyne.



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Wednesday, March 01, 2006

Jan's Scribe Today


Hi guys. My name is Jan and I am today's scribe. Today we had one period of pre-cal and we were reviewing some transformations and translation. Well, we wrote a few notes for our dictionary's.

Sketching Reciprocal Functions 1/f(x)

Remember: f inverse of x does not equal 1 over f of x

Example: If f(x) = x^2-4 Sketch 1/f(x)

Sketching f(x)

Step 1) Sketch f(x)

Step 2) Reflect the portion of the graph of "f" that is below the x-axis above the x-axis

Example Sketch the graph of f(x)=x^2-4

Trigonometric Modeling and Transformation

An Example

For a Saskatchewan town the latest sunrise is on Dec 21 at 9:15am. The earliest sunrise is on June 21 at 3:15am Sunrise times on other dates can be predicted using a sinusoidal equation.

Note: There is no daylight savings time in Saskatchewan

a) Sketch the graph of the sinusoidal function described above

b) Write 2 equations for the function; one using sine the other cosine

c) Use one of the equations in (b) to predict the time of sunrise on April 6

d) What is the average sunrise time throughout the year

e) On what days will the sunrise at 7:00am?

So that about sums it up for todays class. The next scribe will be . . . . . . . . ALDRIDGE

have fun with that




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