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