Towards the end, YAY! (5.4 and 5.5)

This is the video for topic 5.3, regarding how to determine equation for a transformed trigonometric function:) 

This is subscribed by bullcleo1, and presented by James Sousa:) 

In subtopic 5.4-Solve the Trigonometric Function, the only aim is to FIND X. 

-The question can be quite direct, for example: 

1. Solve cos x-1=0, xε[0,2π] 

Answer: 

cos x=1

x=cos^-1(1) 

(scientific calculator time...) 

x in quadrant 1=0

x in quadrant 4=2π-0

                      = 2π

Thus, x=0 and 2π  Note: x cannot be more than 2π. 

-The question can be a bit more complicated, for example: 

2. Solve 3csc² x-4=0 , xε[0,2π] 

Answer: 

3(1/cos²x)=4

(3/cos²x)=4

(cos²x/3)=1/4

cos²x=3/4

cos x= +/- √3/2

when cos x= +√3/2                               When cos x=-√3/2

x in quadrant 1=π/6                               x in quadrant 2=π-π/6

x in quadrant 4=2π-π/6                                                = 5π/6

                      = 11π/6                            x in quadrant 3=π+π/6

                                                                                     = 7π/6

Thus, x = π/6, 11π/6, 5π/6 and 7π/6

The focus in subtopic 5.5 is on determining the instantaneous rate of change. It can be determined by finding the tangent through graphing calculator. 

Normally a table will be given in the question, for exp: 

Time(s)	Volume of air(mL)
0.0	131
0.5	134
1.0	141
1.5	152
2.0	167
2.5	153
3.0	129

and the common questions are:  

a) make a scatter plot 

-which can be solved by key in the data into gc and get the graph

   steps: STAT, 1, key in the data, 2nd, STAT PLOT(on the plot),       

                    Zoom 9, STAT; Move the cursor to CALC;C, Move cursor 

             to RegEQ, Var, Y-vars, 1, Enter, Move cursor Calculate,  

             Enter, (equation out), Graph. and....DONE! :D

  

b) determine the equation

-which can be determined from gc too after getting the graph

c) the instantaneous rate of change at x. 

-can be determined from the tangent, by using gc. 

Not gonna screw up my advance function! :D

As I said in the previous post, I encounter problems when come to solve the some of the questions in chapter 5. Thus, I take initiative to learn through Youtube (that's what a teenager living in the advance technology era should do, make good use of the internet :D). 

And I find a number of nice and kind-heart beings upload their tutorial videos in different topics of Maths to Youtube and fellows viewers just watch for free and benefited from them.(A round of applause for them!) Some of the videos are indeed useful and I really would like to share them with you all who face the same difficulty as me, sharing is caring, right right:D 

Below is the basic Graphing of Trigonometric Function: 

Appreciate the good job done by MathTv. 

Here comes the complicated part! How to graph a transformed graph. 

Credits to this awesome teacher, PatrickJMT :) I LOVE You! 

Chapter 5 is not a piece of cheeeseee cake:(

Encounter some problems and difficulties when solving some problems in chapter 5. It started off well, chapter 5.1 only requires us to know the shape of the graph of basic cosine, sine and tangent function, and determine the amplitude by using the formula (max point-min point)/2, period by using the formula 2π/k, vertical translation by using formula (max point + min point)/2 and phase shift.


However, things get a tad more complicated when it reaches 5.2, where the reciprocal of the trigonometric function comes in, that we have to determine the shapes of secant, cosecant and cotagent graphs.  Besides, there are also questions asking on for exp:  Explain the difference between cot 1 and tan^-1(1). The answer should be cot 1 is the reciprocal of tangent, where as tan^-1(1) is the inverse of tangent. Nonetheless, 5.1 and 5.2 are still manageable.


When it comes to 5.3, I start to get big headache!

How I look like..

5.3 deals with the sinusoidal function of the form: a sin [k(x-d)]+c and a cos [k(x-d)]+c. We are suppose to determine the amplitude, period, k value, phase shift and vertical translation from the equation, and make the drawing of the transformed function. DRAW is a big NONO for me! Especially when the transformation of the graph involves phase shift. Apart from that, we are also to determine an equation by analyzing a transformed graph given, again, I find it hard to determine the phase shift. ARGH! 


Fortunately chapter 5.4 and 5.5 are much better. We are only to solve for x from the function given in 5.4, and in 5.5, it is the application of trigonometric function to determine instantaneous rate of change. However, both do become kind of difficult when the question is asked in the form of application in real life.

Start anew with...Another Chapter.. 5

In the previous chapter, we have learnt about some basic Trigonometry, including 4.1 Radian Measure, 4.2 Trigonometry Ratios and Special Angle, 4.3 Equivalent Trigonometric Expression, 4.4 Component Angle Formula and 4.5 Prove the Trigonometric Identities.


Chapter 5-Trigonometric Function is the continuation of the last chapter. However, it does not deal much with the measure of angles, but it involves and focuses more on the drawing of cosine, sine, and tangent graphs, analysis of the different kinds of graph such as the amplitudes, period, phase shift, and vertical translation, and also application of the trigonometry function in real life, such as determining the instantaneous rate of change.

Apply trigonometry function to real life, let's dance!:P 

Blended learning the Power Function:D

I suppose that blended learning should be a phrase that is familiar to all the cpu students as we just had it yesterday. Yea so basically on that day all of us do not have to attend to school but just complete the assignments teachers posted on BB7.(sounds easy huh:D)

Since Taylor's College CPU programme is advocating this system to providing the highest quality academic preparation for students, it means we are actually encouraged to search in the net for some useful videos or even games in order to help us succeed in a certain subject. So, let's begin with blended learning Advance Function through youtube which is the most common website we use to search for songs and mv! :)

Here is the first video on the general idea about what power function is: 

As what the man in this video said, the general form of power function is y=xn where n=any real numbers, regardless of the sign and value. 

Next, check out this video to look at how to find a domain and range of a function graph. 

So basically, domain=set of possible values of x , range=set of possible values of y. x is often known as independent variable where y is dependent variable. It means we are free to give any values to x, whereas the value of y will depends on the value of x. 

Besides range and domain, we are often asked to describe the end behaviour by analysing the graph.  There are two ways of writing the end behavior of a graph. 

(1) Describe the extension of graph from which quadrant to which. 

Exp1:

 This graph shows a 'Smile' graph, thus we know that the leading coefficient will be positive. So when we describe the end behaviour, we would say the graph extends from quadrant 2 to Quadrant 1. (as the graph starts from quadrant 2 and ends at quadrant 1). 

Exp 2: 

As the graph shows a 'frowning' sign, we will know that the leading coefficient is a negative value. So the end behavior of this graph is, the graph extends from quadrant 4 to Quadrant 3.

Check out the video of this awesome man to learn the second way of writing end behavior which is by using set notation:

That's all for today.Lastly I hope that we all have a nice time learning advance function.

Watch this video to release your stress. Funny video of super awesome maths teacher! 

                                                      Enjoy yourself, have fun all!:)

-Jessie-

Advance Functions@CPU ..

This is already the third week for me being in CPU and things are getting better each day. As most of them say, CPU is the best and awesome among all with all the experiences that we could hardly possible to get in the other programmes:)

So well, today is the exactly 10th lesson we have for Advance Functions( Nice figure though) since 19 July, and we are already halfway on Chapter 1, learning polynomial function. Supposedly functions should be something that is quite familiar for us since most of us studied that in Form 4. Nevertheless, this not just functions, but Advance Functions.

And therefore, the difficulties are there especially when we were introduced to some new terms for exp power function, end behavior, interval notation, finite difference and etc( I am sure that there will be more to come).

Things get tougher when we have to learn to operate Graphing Calculator since this is completely a new device for us and is very different from the calculator(570ms, 570es) we used last time. Especially when sometimes we follow all the steps correctly but the word

ERR:SYNTAX keep on appearing and can be pretty annoying. And later I found out that most of the time this problem occurs is because the cursor is not moved to the right place. Guess we all still have to take time familiarize with it.

There are definitely still a lot more for us to explore, discover and learn throughout this semester for Advance Functions. So Yeah, we are ready for it!:)

-Jessie-