TEST THURS

Spend the class going over the review test; reminder that the test is on Thursday. We will be starting chapter one tomorrow.

Sinusoidal Word Problems con't

Continued work on sinusoidal word problems. We will finish this off during one period of the double tomorrow, and continue with chapter review in the second period, thus completing this chapter.

I realize these problems don't necessarily come "easy", but please don't give up on them too easily.
Believe it or not, you use "words" everyday in real life!

The key things you are trying to do here is change the word problem into a graph. Once you have gotten that far, it's just like all of the other problems we have been doing. In particular, you are looking for these values:

MAX
MIN

You need a maximum and minimum value to solve these problems. They are there in the problem, you just need to find them. Look hard. Use binoculars if you need to. Don't give up!

Here are some of the problems we solved in class. Homework was the completion of the sheet we did in class.

Sinusoidal Word Problems

More practice on changing the graph into an equation yesterday, and the beginning of sinusoidal word problems.

Pictures posted above From Tuesday's class. Sorry for the delay in uploading them; my camera had been misplaced.

Homework for tonight was Q2,3,4 from the homework sheet on word problems.

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.

SA/Amplitude/Period <-> Equation (now with HW!)

Our final topic in this chapter has been using the period, sinudoidal axis, and amplitude to find the equation of a sinusoidal function.

The homework questions were copied down in class, but I will put a photograph of them here on Saturday.

(Refresher)

The sinusoidal axis:

• y = (vertical translation), or
• y = 0 (if there is no VT)

The amplitude

• equal to the vertical stretch
• equal to 1 (if there is no VS)

The period

• equal to 360 * (horizontal stretch)
• equal to 360 (if there is no HS)

Keep in mind going from the transformations to the equation requires you to take the reciprocal (if there is a stretch) or additive inverse (ie change the sign, if there is a translation)

eg. For a graph of the function y=sinx with a HS of 1/3 and a VT of 4, the equation is:

y - 4 = sin[3x]

HW from front board: Find the (a) transformations and (b) the equation of the graph of y=sinx which has ...

i) Period of 180, sinusoidal axis of y=2, and Amplitude of 4
ii) Period of 120, Maximum of 6, minimum of -2
iii) Period of 90, Maximum of 2, Minimum of 6

Finding roots of a sinudoidal

Ongoing homework:

a) Complete six questions from Friday's HW (if you have not done so already)

b) p.143 #30 D.F.G.H

QUIZ TOMORROW - Graphing sinusoidal functions

'Today was a bit of review on how the topics of the past week all fit together.

Homework: For each of the following sinusoidal functions ...

• List the transformations on either y=cosx or y=sinx
• Find the mapping rule
• Create a table of values for one period
• Sketch the graph
• Give the equation of the sinusoidal axis, the amplitude, and the period

-(y-2) = sin[2(x-30)]

(1/2)(y+3) = cos[(1/3)(x+45)]

-2(y+1) = sin[(1/2)(x-60)]

There will be a quiz on this first thing tomorrow.

Quiz plus transformations from equations

The past few classes we have been studying what effects transformations have on the graphs of y=cosx and y=sinx.

Today, we investigated dtermining the transformations from the graph of y=cosx and y=sinx. This is very closely related to the work in grade 10 on transfortmations.

For practice, homework is p.111 #14(a-e) and #15 (a-b)

For these questions, I just want you to [a] list the transformations on the graph of y=sinx, and [b] state what the mapping rule would be.

Sort Quiz Wednesday

There will be a short quiz on Wednesday, related to the assignment, to be handed in on the same date. Given transformations of the graph y=cosx, find:

• Mapping rule
• Table of values
• Sketch the graph
• Sinusoidal Axis, Amplitude, and Period
  

Transformations of sinusoidal functions

Double Period today.

First period involverd looking at the affect horizontal transfortamtions had on the graphs of y=sonx and y=cosx; including the period, sinusoidal axis, and amplitude.

Second period involved correcting work from the first as well as reflections and putting all of the transformations together.

Homework: for each of the following,
a) Find the Mapping Rule
b) Table of Values
c) Graph the function
d) Find the period, sinusoidal axis, and amplitude

1) y=cosx with a reflection in the x-axis, horixontal stretch of 1/3, horizontal translation of -180
2) y=cosx with a vertical stretch of 3 and a horizontal translation of 90
3) y=cosx with a reflection in the x-axis, vertical stretch of 1/2, horizontal stretch of 2, vetrtical translation of 1, horizontal translation of -90

Transformations of sinusoidal functions

Started the class with a quiz on Period, Sinusoidal Axis, and Amplitude.

The goal of tonight's homework is to find the mapping rule, table of values, amplitude, period, and sinusoidal axis for the first six graphs from the previous night's homework.

I'm hoping we can extend that homework on Monday to find a relationship between the transformations (Reflection, Vertical Stretch, Horizontal Stretch, Vertical Translation, Horizontal Translation) and the properties of sinusoidal functions (Amplitude, Sinusoidal Axis, Period).

It is important that you make a solid attempt on this homework for Friday, because we are going to run with it on Monday (bring track shoes if necessary).