Extra - p.156 Solutions

Some selected solutions I worked out to questions on p. 156 #20.

solutions for review Q's coming - TEST WED

Today was mainly a review of word problem questions (sorry, no pics). I'll post up the solutions to some review questions from the book later this evening.

TEST WEDNESDAY

Continued working on sinusoidal word problems today, essentially wrapping this chapter up. First period of the double on Monday I will set aside to correct homework and for you to ask questions. I will also put solutions to the compliment conjugate problems from Wednesday online, as well as any others requested on the message board.

Forgot to snap pics of the solutions today, so I'll post those tomorrow. Here is a brief overview of what is on the test text week, as posted in class. The only thing missing are the compliment conjugate questions. Ignore the stuff on the right. Of course, a nicer, less eye straining version is in class.

Fermat test on Friday, remember some of the strategies we discussed in class. They might not all show up, but it is a good place to start.

Sinusoidal Word Problems

Sorry for the late update, had an issue with misplacing my camera. Turns out it was in my pocket.

.........

Anyway,

Yesterday's lesson was dealing with rationalizing denominators using the conjugate. Essentially, this deals with when you have something like (root)3 + 1 in the denominator and you want to rationalize it, using the theory being the difference of squares.

Today's work was sinusoidal work problems. We will be continuing this and finishing it up tomorrow.

Reminder that the chapter test is going to be on Wednesday. Some solutions for homework are posted above. Homework for tonight was the first page of the word problems sheet handed out in class. Fermat test will be on Friday (we discussed strategies for these questions as well)

Graph -> Equation

Some notes from today's class about changing the graph of the sinusiodal into an equation. Test is next week. Homework is at the bottom of the page.

We'll continue with word problems on Tuesday, as well as reviewing Fermat strategies.

Test solutions

Here are written solutions to questions 1 and 2 (a-f) from the test. You don't need to change radians to degrees in question 2, but I just did it for those who aren't certain where the numbers are coming from.

You can find a copy of the unit circle here.

Extra questions in the vein of these topics on p.170 #1.

Extra Help - Identities

As requested on the message board, here are solutions to 15.b and 15.c on p.155.

Identities are tricky, mainly because there isn't one certain strategy that will "always" work in order to find you the solution. You may find it helpful to adapt the following strategies as a plan to tackle identities. Ask yourself:

1. Are there any common factors?
2. Am I adding fractions? (find common denominator)
3. Are there any Pythagorean Identities that can be simplified?

If you try all of this and still don't have both sides equal to each other, then change everything in the problem into sines and cosines:

cscx = 1 / sinx

secx = 1 / cosx

tanx = sinx / cosx

cotx = cosx / sinx

After you have done that, if you have still not arrived at the solution, go through steps 1-3 one more time. Almost every question you will encounter in this course can be simplified using this strategy.

If you want some further practice beyond the identities on p.155, I suggest p.171 #14 a,c,e,f

The review questions assigned previously in class (a few posts down) are also good practice. The quiz is ONLY on chapters 4 and 6 - no sinusoidals this time.

SUPER QUIZ MONDAY

A reminder that the super-quiz (chapters 6 and 4) will be on Monday.

If you are having difficulty with any specific questions or subject areas, post a comment either here or on the message board by Friday night, and I will write up some notes to assist you and post them here on Saturday.

Review + Homework (SUPER QUIZ THURSDAY)

The Review questions and homework (5 questions) are in the attached photos.

A review quiz will be held on Thursday. Due to this, checkpoint #2 for the independent study is delayed until Monday.

Review Homework

Please use the long weekend to try and clear up any aspects of the course you are having trouble with up to now. We will be doing some review on Tuesday during one of the classes in antipication of a major quiz on Wednesday. If you are having some troubles, come with specific questions for Tuesday.

The weekend homework assigned is pictured above (the flash is covering "3cos")

Roots of a sinusoidal + graphing

Last class was putting everything together we have been studying for the past few classes. Homework (which is due Friday); for each of the following four functions:

• Find the transformations of the graph y=sinx or y=cosx
• State the mapping rule
• List a TOV for one period
• Graph the function
• Find the roots
• State the equation of the sinusoidal axis, the amplitude, and the period

(1/2)(y+1) = sin(x+90)

-(1/2)(y-2) = cos(3x)

-4(y+4) = sin[5(x+30)]

-(y-1) = cos[1/2(x+3)]

Todays class will be in-class work on the independent project. Next checkpoint date is THURSDAY, NOVEMBER 16TH.

Finding roots of a sinusoidal function

Homework: p.146 #37,39,40

Transformations of sinusoidal functions con't

Corrected work on sinusiodal functions from Thursday. In addition:

create a Table of Values and sketch:

1/2 (y+1) = cosx
1/2 (y-1) = sinx
y + 0.57 = sinx
y + 0.15 = cosx
1/5 (y + 4) = sinx
1/3 (y - 4) = cosx

then do:

p.144 #31a,b,d

You may see a relationship between the answers from these sketches and your solutions to these questions ....

(how cryptic!)

Indepedent Study - Checkpoint #1

Today was the first checkpoint date for the independent study. Students are expected to have at least 40% of the work for this project completed by now.

I am very impressed with how everybody is progressing in their projects so far.

The next checkpoint date is November 24th. Groups are expected to have at least 70% of their project completed by this date. Some things I will be looking for in particular for the next checkpoint:

• You should have a complete understanding of exactly how you will be presenting the project.
• You should have some work done on your final presentation material.
• You should have a solid understanding of the mathematics behind your project, and what you will be showcasing.

I am definitely looking forward to seeing these final presentations, and plan to invite some other math teachers in the school to come sit in on them. If you are curious about what your classmates are working on, here is a list of all the projects:

• The History of Pythagoras
• The Mathematics of Gambling
• Triangle Centres and Circles
• Mathematics and Music
• The History of Fibonacci and the Fibonacci Sequence
  
• Napolean's Theorem
• The Golden Ratio
• Number Systems
• The History of Pi
  
• The Monty Haul Problem (Let's Make a Deal!)
• Creating a Sundial
• The Platonic Solids
• Morley's Miracle
  

Homework from Thursday will be discussed on Monday.

Transformations of sinusoidal functions

(Message Board is coming)

Discussed transformations of y=sinx and y=cosx and how they relate to the original graphs.

Homework: for the following equations, find the (a) Mapping rule, (b) Table of Values, (c) period, (d) sinusoidal axis, (e) amplitude.

i) (-1/3)(y-3) = sin[ 2 (x-15)]

ii) -2(y-2) = cos [ (1/3) (x-270) ]

iii) -(y-1) = sin [ (1/2) (x+45) ]

iv) 2y + 4 = cos (3x + 180)

Reminder:

• Sinusiodal axis is y = (VT)
• Amplitude is VS
• Period is 360 * HS