## Going round and round until you are dizzy

Trigonometry is all about circles – from the start to the end of your study in this maddening topic, you will be coming back to the same point: circles. In other words, you will be getting dizzy:

The Unit Circle is part of your previous studies, and you are expected to undestand it at this time. For those of you who need a refresh on this topic, here are a few links (1, 2, 3, 4) (note that 3 and 4 are particularly good!)

This year, we continue to look at the three primary trigonometric functions, and the ways in which they can be distorted (either by stretching, compressing or translating them). The basic form for all trigonometric functions is below (we’ll use sine as an example)

y = a sin (bx + c) +d

where:

**a** = vertical dilation/compression (amplitude)

**b** = horizontal dilation/compression (period)

**c** = phase shift (horizontal translation)

**d** = offset (vertical translation)

This means that:

As you increase **a** (>1), the amplitude (height of the sine function) gets larger (and inversely, as you decrease(<1) **a**, it gets smaller). Note that if **a** is below zero, the graph inverts

As you increase **b**, the period gets smaller (you have more “complete” sine function waves in the same space). As you decrease it, the period gets larger. Note that a negative value for **b** also inverts the graph for sine

As you increase **c** (>0), the function is shifted to the right and and as you decrease it (<0), it is shifted to the left.

As you increase **d** (>0), the function is shifted up, and as you decrease it (<0) it is shifted down.

You can see how the graph of the sine function is altered by each of the variables a – d by experimenting with these animations

Here is the start of a video sequence that will review the information you need to master. The videos are in total 2 hours long, so be smart and preview each one to make sure you are spending your time effectively.

The rest of the playlist is here

Finally, some notes to support and explain the text book sections better. (1, 2, 3, 4)

And, of course, the checklist for all of you – remember you are expected to complete this before you return to school.

See you in class next week!

ps. Don’t forget your MathsOnline Tasks – only four of you have finished so far…

**Explore posts in the same categories:**Mathematics

July 18, 2010 at 11:18 PM

Hi sir, do you have any math online stuff that deals with domains of circular functions, i still have trouble when you convert x to theta and then appropriately changing the domain to suit theta.

July 19, 2010 at 7:47 PM

Hey Sir can you please post any links for practice tests for circular functions?

April 10, 2011 at 9:21 PM

[…] Read the posts on Circular Functions (1, 2) […]

August 7, 2011 at 10:03 PM

[…] There is a previous post on CyberChalky that goes into much greater detail – you may want to check it out. […]