Nov. 30 Class

Congratulations on completing the Unit Test!
Here's the next unit:

Sinusoidal Functions

Handouts

• Daily Plan
• Periodic Functions

We started by discussing period functions today.  Those are functions that repeat themselves over and over again.  They describe things from amusement park rides to the changing seasons to sound and even light.

We then looked at various functions and decided if they were periodic or not.  Here are some functions that are periodic:

You can find a regular interval over which the graph repeats. 

If you can find a repeating pattern over a regular interval, then it is periodic.

The red line is the base graph of what we will be sketching this unit. 

The following are NOT periodic:

Not periodic because the intervals are not regular.

Not periodic because the maximum and minimum values change.

Not even a function!

The circle is not a function, but if we were to graph the value of the y coordinate as we move around the circle, we do get a periodic function!  See the GIF below:

How a sine graph can be generated from a circle.

We will learn much more about this graph in the days to come.

Homework: Complete the handout, P. 352  #1–4, 5ab, 6ac, 7–10

Nov. 26 Class

Today we took up the formative quiz that I handed out last week.  Here are the solutions:

Here is an additional example of how to solve quadratic forms of trigonometric equations.

And finally, here is a new handout of word problems to practice on:

Handout: More Word Problems

Homework: Complete handout, P. 338 #1–13

Some solutions

As promised, here are solutions to the Thinking Questions on the Formative Quiz:

And here is the solution to the last question from the 3D questions handout.

Remember, the test is on Wednesday & Thursday.  Happy studying!

Nov. 22 Class

We had an interesting class today!  We started working on 3D trig problems and came across a very challenging one.  When doing 3d questions it is very vital that you read the question carefully and draw a good diagram.  Be sure you define all variables clearly in your diagram, or define them using a sentence.

Handout: 3D Trig Problems

Here are the notes from today including the solution to the challenging question.

I'll post the solution to Example 4 over the next couple of days.

I also handed out a formative quiz for you to take home and try.  We will go over the quiz on Monday.

Homework: Complete handout, complete formative quiz, P. 332 #3–9

Nov. 21 Class

Today I went over some problems from yesterday's homework.
Here are the notes:

Next we talked about Cosine Law and some of the uses.
Here are the notes:

Homework: P. 325 # 3–11

Nov. 20 Class

Today I gave more practice on solving trigonometric equations.  These are more challenging than the ones yesterday.

Handouts:

• Solving More Trigonometric Equations
• Ambiguous Case

Then we discussed how the Sine Law can sometimes give two possible solutions for a given set of information.  This arises because when we do the inverse of Sine, there are more than one possible solution.

Notes on solving:

Notes on ambiguous case:

Homework: Complete handout, P. 318 #4-14

Nov. 19 Class

Today we talked more in depth of how to solve simple trigonometric equations.  Remember, there are multiple solutions when you are solving for angles, therefore, you must use the CAST rule to find which quadrant the solutions are in.

Handout: Solving Trigonometric Equations

Here are the examples I did in class.

Homework: Complete worksheets

Nov. 16 Class

Today we looked at the the case of how to define the Primary Trigonometric functions when the angles are greater than 90°.  For example, what is sin(225°)?

We certainly can't draw a triangle and find the ratios of opposite, adjacent and hypotenuse because it's difficult to draw a triangle with a 225° angle!

To find sin(225°) we actually need to define a few more things and that's what took the majority of today's class.  For now this is a lot of terminology and technical work, but we will find that it is very practical when it comes time to solve different types of problems.

Handouts: CAST Rule

Here are the notes:

Homework: Complete handout, P. 299 # 1-12

Nov. 13 Class

Congratulations on completing the Unit 4 Test!

I surveyed the class and about splitting the test over two days and here are the results:

• 1/3 in favour
• 1/3 against
• 1/3 don't care

After weighing all the factors, we've decided to stick with the two day testing.  I will make sure the next test is back to back to avoid having days in between.

Unit 5 Trigonometry

Today we began with reviewing trigonometry, as well as introducing the reciprocal trigonometric identities.

To catch up to the other classes, I also introduced the special triangles.  These are the triangles that are in all your geometry sets!

They allow us to write down the exact ratios for any of the special angles.

In the table U stands for "undefined".

Here is the handout from today: Special Angles

Homework: Write notes for performance task.  Complete handout.

Nov. 6 Class

Hello Class,

Some of you may have heard rumours that I will be away for the test tomorrow... I have to say that those rumours are in fact... true.

No worries though, I know that you guys are a strong class and will do well without me.  Remember the test will be split into two parts.  Knowledge and Thinking is Wednesday followed by Application and Communication on Monday.  I will be back for the second part.

Topics to be covered:

Knowledge & Understanding
Be able to...

• Simplify exponents using appropriate rules.
• Rewrite rational exponents as radicals and radicals as rational exponents.
• Know the characteristics of exponential functions.
• Graph exponential functions.

Thinking

• Challenge questions.  Sorry, no clues!

Application

• Graph exponential functions with multiple transformations.
• Solve equations with exponentials.
• Solve word problems involving exponential growth and decay.

Communication

• Describe some exponential function or mathematical procedure with exponentials using words.

Here are notes from yesterday:

Here are the handouts:

• Exponential Growth and Decay Problems
• Formative Quiz
• Formative Quiz Solutions

Textbook work:

P. 263 #10-16

P. 267 #1-17

P. 270 #1-7

Good luck!

Nov. 2 Class

Today we began by working on horizontal stretches of exponential functions, but then a majority of the class complained it was too easy!  So we moved on to discusse word problems and applications of exponential growth and decay.

Handouts:

• Investigating Transformations
• Transforming Exponential Functions

Here are some examples of horizontal stretches and compressions:

And just for fun, here are all the possible reflections:

Remember that bases can change too!

You all complained for more difficult examples, so here is one.  Try to sketch the following.

The first step is to use the exponent rules to rewrite the expression in a more recognizable form.  Then you can write out the transformations and you should get this graph:

Exponential Growth and Decay

Things that grow and decay can be modelled by exponential functions.  I told a story of a man who goes to ask the Emperor for rice.  He asked for one grain of rice on the first square of a chess board and asked to double it on each adjacent square until the board was full.  What function would model the amount of rice in each square?  The answer is an exponential function of base 2.

Here are the notes I gave in class:

This example was meant to show you how the general formula was derived.  Once you know the general formula, you should it from now on. 

This will model all the examples of exponential growth or decay.  In the case of exponential decay, the formula would contain a negative 'r' value and it would be called the "decay rate".

Homework: 

• Complete all graphing worksheets.  
• P. 251 # 1-11 
• P. 261-263 # 5-11