Thursday- October 29th, 2009

Well guys, today was our test day on the Identities unit. I sure hope everyone studied hard and went over the pre-test a few times. I believe that helped me with the actual test because it was practically the same. Awesome? I think so.

Test Help

First off I really don't care about the facebook group so if people want to make it giver. I also was getting ready for the test tomorrow, I've been looking through that green book we were told to get at the start of the year. I have found it really helps, it explains stuff really clearly, so I would suggest picking that up to all of you who don't have it. That is all.

Study Period

We got our test on Transformations back today, and it was an alright turn out. Some people did very well, and some not so well. Oue test on Identites is tomorrow and this class gave us a bit of time to prepare and ask questions. Although some of us chose to look at halloween costumes, we found it was a successful day.
Happy Halloween Everyone

Trig Identities / Double / half angle identity

We talked about making a group to follow on Facebook. Personally i'm not a big fan of Facebook or any blogging sites... I rairly use it and when i do i tend to get keylogged. Needless to say i give this idea a big thumbs down.

We did a review on double/half angle identities for the test on Thursday.

Everybody Loves a Work Block!

Today Mr. Max gave us the wonderful news that this block would be a catch-up block so that we can finish up our Exercises. Do your homework! Theres going to be a homework check at some point this week, and since it's randomized, it's better to have everything done. If every exercise is done, there's no chance you'll have the bad luck that the calculator will pick the ONE exercise you didn't do. Because thats how it always happens right?

So don't forget:

• Homework Check this week from Exercises 11-19!
• The test was moved to Thursday so study study study!
• Go hit up tutoring on tuesday with Mr. Max and wednesday with Mrs. Larson if you have any questions or worries about the upcoming test!

Trig Identities - Sum and Difference

Today we continued on with the Trig Identities unit and into a section called "Sum and Difference Identities". Today basically consisted of us learning six formulas using sin, cos, and tan; and how to solve angles that we are unfamiliar with, such angles as 7pi/12 and tan(75) (for the formulas, refer to the formula sheet. All these formulas will be given to us on the final exam, so know them, DON'T MEMORIZE THEM). A sum and difference question can be looked at as being a 2 part question. What I mean by two part question is that there is more that one piece to the problem, and furthermore by piece I mean angle. Up until now we were familiar with angles like pi/6, pi/4, pi/3, etc....... and never really thought of having a twelfth of a pi. Now comes the thinking part. "I don't know a thing about pi/12, but since this angle can be thought of as a 2 angle identity, mamby two angles I already know can add up to a twelfth..!!" Now we are on to something, two angle we know are pi/3 and pi/4, and added together equal to 7pi/12. Well that seems pretty easy some would say, but some question will take a little more effort that that to be solved. Unfortunately the only way to come about finding these answers is by educated guessing and checking. Mr Max said that solving identities was like doing a puzzle, so let the puzzle sloving begin. Use the angles you already know on the unit circle and take some previous fractions knowledge, put them together to figure it out. when you find the two angles that add together or subtract from each other, go to the formula sheet and find the corresponding formula. when you have the formula, set one angle to alpha and one to beta, AND DO NOT SWITCH THEM AROUND. Plug the alpha value into everywhere the alpha symbol appears in the formula, and do the same for the beta value. from here all you are solving for now is exact values that come strait off the unit circle. Follow throughout the formula and complete all the algebra taking into consideration the order of operations, and eventually you will end up with an answer. (haha I know, convincing eh??) The trick is practice, and the must is remembering algebra rules.

If you need help ever and don't have a teacher or tutor at your right hand, there is a new sight on the net called wolfram alpha (http://www.wolframalpha.com/). this site virtually lets you type in any mathematical question and it gives you the answer in about 15 different ways, and it can even graph it!! try it out for yourself and see what wolfram can do for you!!! This has been a paid advertisement for wolfram alpha inc. jkjk Mr. Max told me to put it on. so i did....

Anyways, The homework for today was Exercise 16 #1-15, but omit #3 & 5, and remember that there will be a homework check sometime next week on the lessons 11-20.

More Trig Identities

More trig identities, more examples, more fun.
Extraneous Roots is what we're doing today. It is the principle for checking trig identities by substituting your answer into your original equation, either for x or theta. "Sounds good on paper, like communism?" Not all solutions in equation are viable and that's why we do this. So an extraneous root is a solution that we get but doesn't work when checked.
We also did our third mental math today.
No new homework, just work on our old assignment (exercise 15: 1-14)

Trig Identities (more notes, examples,etc..)

Mr. Max says that trig identities is basically the same as solving puzzles in class
there is never the solution only a solution

Techniques to assist proving identities

1.reduce (simplify complicated side to try to "match" the simpler side)

2.work each side independently to some intermediate expression

3. DO the addition / subtraction of the rational expressions.

4.DO the multiplication / division of the same rational expressions.

5. Simplify GCF's ALWAYS (ie. factor if you can)

6. Factor, Factor, Factor

7.try multiplying both numerator / denominator by same expression to get to know identities.

8. IF possible? rewrite all trig. functions as sin(x) or cos (x);look for patterns

Todays assignment is exercise 15 questions 1-14

Trigonometric Identities

At the start of class Mr. Maksymchuk let us explore the internet to find out what trigonemtric identities are. He gave us a list of trigonometric identities and gave us an example using them. The way I understood it was that trigonemetric identities are the different patterns showing the similarities between the different trig functions. The Mickleson book has some good examples that helped me to understand it.

Work Period

Today we were given the period to work on our Accelerated Math and were assigned to do Exercise #12, 1-11 and Exercise #13, 1-10 (Homework check on Monday). I really appreciated having time to catch up in class and work. When I was studying for the test Tuesday night, I found the 'Online Version of This Class' link on our blog a lot of help. For me those practice 'exams' on each unit is a really good review, it has a little bit of everything and it's really good practice. We all have the potential to do super well, we just need to keep trucking!

"The difference between try and triumph is a little umph."
-Author Unknown

Test #1...

We got our first test back today. If you were like me and didnt do so good thats ok because Mr. Maks has allowed this test to "disappear". As long as we learn the information by the end of the course that is what matters. We also got the pre-test answers today, and i think it is an excellent idea to go through that because i found that for the first test the questions on the pre-test were very similar to the questions on the actual test. And accelerated math is another way to prepare for tests. If you can do the questions on accelerated math, you will most likely be able to do those questions on the test...thats what i found to help me out anyways.
TEST TOMORROW...good luck guys!

Homework Check

Today, Mr. Max went down to the cafeteria and almost everyone got to go down and show him their homework and talk about how they are feeling about the course. Have a good weekend everyone....Dont forget to study for the test on Wednesday.

Transformations- Absolute Values

Today we learned how absolute values can be understood as a piece-wise function (the function can be split into one or more pieces).

Definitions of an Absolute Value:
|x|= x if x is greater than or equal to 0
|x|= -x if x is less than 0

Example: When graphing y=|f(x)| :
|f(x)|=f(x) if f(x) is greater than or equal to 0
|f(x)|= -f(x) if f(x) is less than 0
The domain of |f(x)| is the same as the domain of y=f(x), but the range of y=|f(x)| will be f(x) is greater than or equal to 0.

I don't think I am making any sense... so I found this website that may help.
http://www.analyzemath.com/Graphing/Graph_Abs_Val_Func.html

Assignment: Exercise 11, Questions 1-12

Reciprocal Functions

Recripocal functions can be defined as;

a/b --------> b/a

In today's class we learned the basics of a reciprocal function. Mr. Max refreshed the class on reciprocals using some grade 11 examples, learned that a reciprocal function is one in which the numerator and denominator switch places, and learned algebraically how to do this. The tricky part came when we put this thing onto a graph!! The graph of a Reciprocal function, compared to it's initial function is curved and has one or more asymptotes along the x axis. The asymptote of the reciprocal function is found where the initial function crosses over the x axis (the x intercepts). Near each asymptote the reciprocal function behaves in a manor opposite to the initial function. What this says is that if the initial function increases as it approaches the asymptote, the reciprocal function will curve off and get smaller as it approaches the asymptote. Similarly, if the initial function decreases, the reciprocal function will increase. The terminology given to was GREATERING and LESSERING (this is a "mathematical technical term" and is not real english, haha). the most important part to remember when deciding whether each function greaters or lessers it to read in the same direction to or from the asymptote. If you read it differently and switch directions at any time, none of the graph will be correct.

October 5th, 2009- Compress/Stretch of a Function

Well, we kicked off this class with a bang. By a bang, I mean mental math.

Following this, we learned about transformations. Specifically, "various compresses & stretches of functions affecting graphs summarized by:
1) y= a*f(x)
2) y= f(b*x)

Here's all the notes Mr. Max wrote explaining all of this today:

I hope this means something to you guys.. Homework is Exercise 8, questions 1-10.

Today we started a new unit called Transformations or Transformational Geometry. We did notes on all of the reference functions, and found the graphs we needed to know off either graphmatica or your calculator. We learned that if one of the reference functions were to slide it would only be left, right, up, or down. The equation of a sliding function is y=f(x-h)+k, where the h value represents left or right movement and the k value represents up and down movement. Be sure that when there is a question in this form that the sign infront of the h value represents opposite slide movement. ie)f(x-5)+3, the h value is -5 so you move right five units.
Check out transformations on ronblond.com, it seemed to be useful seeing the tranformations on the graphs and which movements slide which direction.

My trig question.

Mine is question 16 from the 2007 pre-calc exam: http://www.edu.gov.mb.ca/k12/assess/archives/pc_sb2_jan_07.pdf






















The answer to this question is d), because:

secθ / tanθ * cotθ = (r / x ) / (x/ y * y / x ) = (r / x) / 1 = r / x

therefore, it remains secθ. And, secθ = 1 / cosθ since secθ is the inverse of cosθ.

september 21st

This is a late post, and I apologize for that. Anyway, Mr. Max taught us more about solving trigonometric ratios. (I'd post pictures, but there isn't any: you can find them in a .pdf file in the coursework drive.)

Also, I dug this up. I'm not sure if we already posted this link. It contains practice exams and explanations and questions for every unit in this course:

http://www.math40s.com/ <That link is quite useful.

I hope you use it. Also, we ought to take a look into Student Workbook for practice. I'm so confused at this point, so I'll need to practice some of the material and find a way to get caught up (hopefully, I'm the only one in this camp). :)

Graphing Trig Functions

So last class we were "tieing ends" on how to graph trig functions. Some definitions you might call them, are period- which is the smallest horizontal space within which repeats itself exactly once. A period of sin (sin curve, cosine curve) equals 2 pi/ b. Your domain is you x value, and your range is where it crosses the x axis. An exapmple question is f(x)=asin(b(x-c))+d. "a" tells us that it stands for the amplitude(which is the distance). "a" value tells you the amplitude.The period is how many times it makes a complete cycle in one cirlce. So the sine or cosine function- 2pi/b or 2pi/period=b. Tangent function = pi/b which also = period.(talking about how much horizontal space it takes up).
When written y=asin(b(x-c)+d c is A PHASE or HORIZONTAL SHIFT.