Nov. 26 Class

Today we did a formative quiz and took up the solutions.

Here is a copy of the quiz: Unit 6 Formative Quiz

And here are the solutions,

Homework: P. 380 #1-6, P. 383 #10-15, 25, 26

Nov. 22 Class

Today we put all our transformations together and graphed a sine function with stretches, compressions and translations.

Handout: Transformations of Sine

Here are the notes:

Homework: Complete the handout, P. 328 # 1 – 12, skip #3.

Nov. 21 Class

Today we discussed stretches and compressions of the sine function.

Here is the handout: Stretches of the Sine Function

We also took some time to go over the handout from yesterday.  Here are the notes:

Homework: P. 373 # 1–18

Nov. 20 Class

Today we discussed how to transform the sine function.  We looked at vertical and horizontal translations.  Vertical translations take the form:

and horizontal translations take the form:

We then practiced sketching some examples.

Handout: Translations of Sine

Here are the notes:

Homework: Complete the handout, P. 365 # 1-13

Nov. 19 Class

Today we continued with looking at the sine function.  We did some more sketching and I showed you how to sketch the sine graph without a table of values.  Here are the notes from today:

Handout: Comparing Sinusoidal Functions

Homework: P. 348 # 1 - 13

Nov. 16 Class

Today we looked more closely at a specific type of a periodic function called sinusoidal functions.  This is the main topic of this unit.

Handouts:

• Waterwheel
• Sinusoidal functions

We began by graphing the height of a nail on a waterwheel such as the one on the side off this house:

Here's a more mathematical diagram:

As the wheel rotates, the height of the nail (located at x) changes.  We graphed this height as a function of the angle and it gave us this:

Get familiar with this shape because we will be graphing it a lot this unit!

Here are the notes form today:

    

Homework: P. 393 # 1-10

Nov. 15 Class

New Unit: Sinusoidal Functions


Handout: Unit 6 Daily Plan

Handout: Periodic behaviour worksheet


Today we discussed what it meant for a something to be periodic.  If a behaviour is periodic, it means it repeats itself over and over again at regular intervals.  For example:

A see saw.

Any ride at an amusement park.

The four seasons.

The vibration of a tuning fork.

When we graph these behaviours over time we get periodic functions.  These are functions that repeat themselves at regular intervals.

Examples:

Periodic: the pointy shape repeats itself every 4 units.

Periodic: Both the red and green graphs repeat themselves every 2 pi.

Periodic: It doesn't matter how complicated the shape is, if it repeats itself at regular intervals, it is periodic.

Non-periodic:  It looks like it repeats itself on the right side, but the left side definitely does not repeat.

Non-periodic: The shape repeat itself, but it is getting smaller each time, so it is non-periodic.

A circle itself is not a periodic function, but if you were to graph the height as you move around the circle, you do get a periodic function.

We then then graphed a periodic function and used it to make predictions.


Homework: P. 330 # 1-13