February 29, 2008

Hello peers,



Today we were blessed to have Ms. Norman step in to keep us all in line, as Mr. Maksymchuk was away today. Ms. Norman informed us that today was to be a work period, simply for us to catch up on any assignment, work on accelerated math, and study for the upcoming test.



After learning how to use graphmatica this semester I have found it very helpful in learning more about graphing and visualizing the "a,b,c,d" values of a function. As helpful as this is I encourage all of you to try drawing the graphs on graph paper also as it will help you tremendously come exam time!



I have also been visiting the Ron Blond site and http://www.math40s.com/ to help me understand concepts and for help in the exercises.



Reminder!!! Accelerated Math is due March 12th so get on your horse and get those objectives done! As well as a TEST Wednesday March 5th!

Image idea courtesy of Lucas...

Remember your times tables, and keep your stick on the ice,

Cramer

The Six Trigonometric Functions Calculator

This online calculator calculates the six trigonometric functions: sin(x), cos(x), tan(x), cot(x), sec(x) and csc(x) of a given angle. The angle may be in degrees, radians (decimal form) or radians in fractional form such as 2*Pi/5

http://www.analyzemath.com/Calculators/Trigonometry_Cal.html

Hey, today Mr. Maksymchuk went over more trig functions and we looked through ron blonds site.

These references are very useful, especially the website which will clear up most or all of your questions.

Functions: EVEN/ODD Functions and Transformations

First things first: these Sun computers are annoying, awful, awfully annoying, annoying awful, and just bloody slow.

Having gotten that out of the way, I would like to begin my blog post: Mr. Maksymchuk spent almost the entire class lecturing about functions and their transformations. First, he explained to us what a one-to-one function is:

Basically, a function cannot have an inverse if more than two elements in the domain map onto a single element in the range; if it does have an inverse, it is consequently called a one-to-one function since it must therefore have its domain mapped onto its range via a one-to-one mapping.

Mr. Maksymchuk then showed us how to employ this fact to simply determine whether a function has an inverse. We use the "horizontal line test" to do this:

Pretty self-explanatory.

Anyway, we then got to the main part of the lecture explaining what odd and even functions are:

Succinctly put, an even function has the property that f(-x)=f(x) and an odd function has f(-x)=-f(x). On a graph, even functions are symmetrical about the y-axis whereas odd functions are symmetric about the origin - i.e., an odd graph remains unchanged if you rotate it 180° about the origin.

We then applied our knowledge by doing some sample questions:





At the end, Maksymchuk talked about graphing reciprocals:




Mr. Maksymchuk then asked us to prove that 1/f(x) can never be zero. As far as I can tell, this can not be the case since we would have 0=1/f(x), 0*f(x)=1 or 0=1. What do you think?

IB

Ahh.. Transformations..

Class was happily(not so much) started with mental math quiz #5.



For the rest of it Max taught us about TRANSFORMATIONS.

It looked something like this:









Reference functions (also called "parent functions") are, in my own words, the base.. what the function looks like before anything is done to it. If you graph the reference function, then ,in the same plane, graph a transformation to it, it helps to visualize what's actually happening.(example of this below)









These are helpful rules to remember(probably wouldn't hurt to have these memorized somewhere in the back of the ol' nogan)

And finally he showed us a little trick:

-the number of curves in a function can be found easily by minusing 1 from the exponent of x.

For example if the function is y=x^2, it will have (2-1), or 1, curve(s).. and so on, as shown in the diagram above.



That's all for today.. but a reminder to keep up with accelerated math!




Max's dream student..

February 22nd

Well, I didn't make it to school today but through the wonder of the World Wide Web, I can still be the scribe. If anything important math-related happened to occur today, I would ask that one of my classmates would share it, either with a comment or a separate blog post. I found this picture on the Internet and thought it somewhat applicable.

http://talkingtails.files.wordpress.com/2007/10/pi-vs.-i.gif

I think Luke summarized yesterday's class fairly well so I don't need to add much to that. The one other thing I was going to mention is that Mr. Maksymchuk has handed out Accelerated Math sheets to us and he also gave us the scantron sheets. I think everyone understands how to use a scantron sheet, but just in case someone doesn't, I'll give a few pointers. Remember to use pencil only! A good idea is to write your name on it first, then fill in if it is a practice, exercise, or test, then fill in the numbers from the top of your question sheet. After that, it's a simple matter of filling in the answers from your sheet.

Something else I would like to point out is that Mr. Maksymchuk added a window (I think that's the proper blogger term to use) into another Grade 12 Precalc blog. I would advise everyone to check it out as it is an excellent blog (as is ours) and I think it has a lot of good stuff on it.

For the questions assigned from Exercises 5 and 6, I had to use the answer key for the first couple of questions because I either didn't know or had forgotten what "general solution" meant. Here's the dictionary.com definition:

general solution
–noun Mathematics.
a solution to a differential equation that contains arbitrary, unevaluated constants

Basically, it means the whole solution, not just the solution over a set interval. Or that is my understanding of it.

If anyone has any questions or suggestions about making my post better, please leave a comment and I'll try to get on it ASAP.

Bethany

Remember That Time I Thought I Made A Mistake, But I Was Wrong???

Several of you are going to want to thank Anna for her polite, kind, and pleasant demeanour this afternoon. Here's why.....It seems as though in my haste to create a nice little test for you all to practice up your trig./solving/unit circle skills, I probably neglected to do any questions (or assign any, for that matter), that have anything to do with radian measures as decimals. Question 10 on your tests did indeed instruct you to provide your solutions as radian measures, but as Anna so politely stated, "It sort of doesn't seem right to have to learn to do that for the first time on the test." I agree. Question 8, I believe, also had an instruction to use the interval [0, 2pi]. In that case, I have more of a leg to stand on after looking specifically at the answer key to Exercise #4, but the important points are thus:

1. If you feel like you got a raw deal somewhere, sometime, the easy thing to do is complain and be grumpy and never address the issue with someone who can make a difference. The hard thing to do is to state your case convincingly while retaining your composure and some measure of grace. Anna did all of that, admirably.

2. As students, you all have a right to be evaluated fairly and consistently. I take that pretty seriously.

3. You need to go on to your post-secondary studies with the idea that a positive attitude and a sense of humour are at least as important as pure aptitude. The world is full of successful people who understand this very well...

Hope to see you tomorrow to deliver the good news in person (and change a few of your test scores)...

Until then...

RM

Graphing Trigonometric Functions

On Thursday, Feb.21st The class was started by a mental math, Followed by the test written the previous day being handed back with the answer key. With many moans in the air after seeing the test results Mr. Maksymchuck quickly moved on to cover the next lesson, Graphing Functions. Also An important reminder from now on.....RADIANS ARE NOW THE DEFAULT FOR GRAPHS.

Next came Reference Curves with a " how-to" lesson in putting the six trig functions into a calculator or other technological device as shown by the image below. Sec and cot are done like csc meaning sec is (y= 1/cos theta) and cot is (y= 1/tan theta). The definition of Asymptote given on the slide below is also very important to know


Then was a bit Review with the definitions of Domain( the values that x can be) and Range ( the values that y can be)

Next was the actual graphing of the functions on graphmatica and ow it can relate to the unit circle i.e Y=sin(x) is greatest at π/2 on the graph and is positive up until π, which is equivalent to quadrants I and II on the unit circle. The image below was handed out in class and has all he functions on the same graph.


The parabola's are formed by the csc and sec graph's and they touch the greatest value of there corresponding function i.e sec touches sin's greatest values. Also the mostly vertical lines are the remaining function tan and cot with tan being the lines bending to the right going from bottom to top and cot being a mirror image of tan.

Then the class was then introduced /reminded of definitions and formulas for them which are on the slides below. Then at the end of class we were assigned questions 1-15 on exercise 5 and 1-16 on exercise 6. The image to the side was also handed out.

Feb 19

Hey everyone,

Today we began the class with mental math, and moved on to correcting some questions from exercise 4. We corrected questions 15 and 16. We have our first test tomorrow. Here are the worked out solutions for questions 15 and 16:


Solutions:

Good Luck on the Test!

Friday,Febuary 15

In todays class we we were assigned homework on Exercise #4 questions 1-17(all). For this exercise we are to use factoring techniques from grade 10 along with what we learned about the unit circle.

If you forgot how to factor heres a website that will hopefully help: http://www.purplemath.com/modules/simpfact.htm

This site also explains how to solve quadratic equations; here is the link: http://purplemath.com/modules/solvequad.htm

If the sine and cosine in the equations on the homework confuse you remember that you can replace sine theta with y and cosine theta with x then solve the equation. Then when your done turn y and x back into sine and cosine and find the angle measure.
Good luck. (don't forget test on wednesday)

Febuary 13th

Today in class Mr. Maksymchuk explained some more about the Unit Circle. He got us thinking in terms of sinΘ - referring to Y, cosΘ - referring to X, and tanΘ - X/Y. The class was also introduced to more radian measure and learning to think about what quadrants they apply to. While we were reviewing the unit circle we found it handy to think in proportional triangles to find the values for sin, cos, tan etc... We also talked about calculating cosecant, secant, and cotangent.

CscΘ=1/sinΘ, SecΘ=1/cosΘ, and CotΘ=Y/X.

This picture is continued from the picture above. Here we were just applying signs to values in terms of quadrants and the location of the coordinates.

This is a similar question to the one above where we discovered that Theta was in quadrant II because Sin > 0. Therefore sin is "+" and because tangent is a negative value, it cannot be quadrant one because X and Y are both positive.

Remember, here is todays assignment and there is tutoring after school until ten to five with Mr. Maksymchuk.

Thanks,

Cramer

Goals

www.kent.math.edu/~sather/ugcolloq.html

Hi everybody! My goals for this class are to:

1. Get 70% (or higher) as a final grade

2. Pay attention and not get distracted so I don't fail because then I wouldn't graduate which would suck.

3. Keep up with my home work.

Hope you guys enjoy the image. I laughed when i saw it. It reminded me of how i feel about math sometimes.

At any rate heres a website that will hopefully help you: http://math2.org/index.html

Have a Great Year!

Just to add, this is the link to the unit circle java applet, you may find it very helpful,
http://www.wou.edu/~burtonl/trig.html
This is a link to an online lesson on unit circles, it could help if your having trouble.
http://www.bmlc.ca/Math40S/Pre-Calculus%20Math%2040s%20-%20Trigonometry%20Lesson%202.pdf

Goals!

www.estlouis.stclair.k12.il.us

Goal-Setting!

My goals for Grade 12 Pre-Calculus are:
1) Get at least 75%
2) Study at least one hour for each test
3)I won't get distracted by others or by games on the computer

A decent math help website is:
http://www.webmath.com/
Some helpful goal-setting tips are found on:
http://www.mindtools.com/page6.html