### Senior Maths

**Why use Radians and how do they work? **Here is a good explanation from this website:

Why do we have to learn radians, when we already have perfectly good degrees?

Because degrees, technically speaking, are not actually numbers, and we can only do math with numbers. This is somewhat similar to the difference between decimals and percentages. Yes, “83%” has a clear meaning, but to do mathematical computations, you first must convert to the equivalent decimal form, 0.83. Something similar is going on here (which will make more sense as you progress further into calculus, etc).

The 360° for one revolution (“once around”) is messy enough. Why is the value for one revolution in radians the irrational value 2π? Because this value makes the mathematics work out just right! You know that the circumference *C* of a circle with radius *r* is given by *C* = 2π*r*. If *r* = 1, then *C* = 2π. For reasons you’ll learn later, mathematicians like to work with the “unit” circle, being the circle with *r* = 1. For the math to make sense, the “numerical” value corresponding to 360° needed to be defined as (that is, needed to be invented having the property of) “2π is the numerical value of ‘once around’.”

Therefore, I like to think of one circle turn as 2pi radians. That is, 2pi radians = 360 degrees. From this simple equation we can work out the size of any angle in radians or the how many degrees in a given number of radians.

**Revision 2:** Here is a useful video which helps explain the variations of a trig function (especially ** Period** and

**). Click of the pic below to access the short YouTube video:**

*Phase Shift*Another really useful explanation video can be found on YouTube **here**!

**Revision 1**: In class today we reviewed the three main trig functions; y=sinx, y=cosx and y=tan x. Then we looked at how changing the x coefficient altered the y=cosx graph (as this helps us understand a later question in the assignment). For example, the graphs below are of: y=sinx, y=sin2x and y=2sinx. Can you work out which one is which? The answer is given somewhere else on this post 😉

Graphing Trig Functions with Graphmatica – note the gap between sin and x (y=sin x). Note: it is best to goto: **Options–>Graph Paper** and select **Trigonometric** for your graphing with trig functions. Graphmatica works in radian measure.

The Functions Project was handed out in class today and you will need to read through it carefully. There is also key information and resources to help you use Graphmatica for this assessment, including **this one** on YouTube. Please email any questions you have as you work through this project in class and at home.

In addition, sketch y=log x and y=10^x (Graphmatica makes this a breeze but you will have to type up as y=log(x)!) The answers for the three different y=sin functions in the May 14 post are: magenta is y=sin x; gray is y=sin2x (doubles up the frequency of the curve or, effectively, compresses it to repeat twice as often); red is y=sin0.5x (halves the frequency of sin x which means that it is lengthened); and cyan (blue) is y=2sinx (doubles the amplitude or height of the sin x curve). To summarise:

*Magenta*: y=sin x has an amplitude of 1 (goes up +1 and down -1 from the mid-line or x axis of the graph)

*Gray*: y=sin2x squishes the function by a factor of 2. So, the curve is being “cycled” twice as fast as y=sinx. This is shortening the period of the function.

*Red*: y=sin0.5x lengthens the cycling effect of the graph – that is, it cycles in double its length for y=sinx. This lengthens the period of the funtion

*Cyan*: y=2sinx has an amplitude that is 2x as tall. Hint: whatever the “sinx” is multiplied by gives you the amplitude of the function

Note: you can always do a simple table of values to plot the above 4 sine functions. More info on this excellent website.

**April 27:** As we reviewed the week’s work there were obvious gaps – e.g. not being able to identify functions from a set of ordered pairs (a set of x,y coordinates) and a few issues in accessing graphmatica, etc. These areas of weakness do need you to review the work done by referring back to the textbook and your notes. Some more practice examples of identifying functions can be found **here**;

The foundational work in *Expanding* and *Factorising* will be great preparation for the more visual work with Functions. Assessment includes a Project. Details soon, but here a good introduction to work through from mathwarehouse.com:

A **Function** is a unique kind of relationship. There are 4 types of algebraic relationships:

1) One-to-one

2) Many-to-one

3) One-to-many

4) Many-to-many

A Function is either Type 1) or 2) relationship. That is, for each element on the domain there is only one unique element mapped to on the range

hey sir,

any chance of getting a digital copy of the task sheet

thanks

Hi sir what is the equation for normal distribution, the b=x positive minus. equation

Do you mean the formula for the quadratic? Check out the following:

http://www.purplemath.com/modules/quadform.htm

Hi what questions did we have to do for homework

Hi Drew. I got to this comment quite late tonight. We are reading the early notes in Chapter 5 on “rates of change” and including another example. Thanks and see you tomorrow.

Hi Sir,

Kath and Olivia here.

Just writing to tell you that we do not understand the homework given, and will not be able to see you tomorrow as we have previous commitments.

thanks, sorry for any inconvenience.

Cool blog sir!