Earth As A Sphere

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Trigo

PMR learn SOHCAHTOA dy right?

Now Trigo in Form 4 got 3 things to know:
1. unit circle and corresponding angle (IMPORTANT! and hardest to learn)
2. Special angles. (not in SPM, basically is shit unless school teacher decide to kena them)
3. Graphs of sin tan cos

If u look at the unit circle above,
1. it is cut into 4 parts, each part called a "quadrant".
2. the quadrant starts from top right, called quadrant I, then go anti clockwise, quadrant II, III and IV.
3. The radius for this circle is 1 UNIT. So if you draw any right angle triangle that TOUCHES the circumference, you can see that the hypotenuse is FOREVER 1. (Important theory to know if you are working with sin and cos)
4. How to measure angle? Basically the angle is measured from the X-AXIS of FIRST QUADRANT
Example:

a. If you look at the all the circles, all the GREEN colour angles are the ORIGINAL angle formed by the red line and x-axis. (ignore the black line that forms the triangle for now)
If you can see, these angles all start from the x-axis from 1st quadrant and turn until they reach the red line.
b. the BLUE colour angle that you see, is what we call CORRESPONDING angle. As you can see, corresponding angles are LESS than 90 degree, and measured STARTING from the x-axis on its own quadrant. (For first quadrant, ori angle = cor. angle)

c. So original angle in
Quadrant I = 0.000000000001 to 90
Quadrant II = 90.0000000000001 to 180
Quadrant III = 180.000000000001 to 270
Quadrant IV = 270.0000000000001 to 360 or 270.00000000000001 to 0

d. Relationship between cor and ori angle
In Quadrant I, ori = cor
Quadrant II, as you can see, ori + cor = 180.
Quadrant III, 180 + cor = ori
Quadrant IV,  ori + cor = 360.
(Different book give different rules, actually is just 搬来搬去 only, like quadrant II they give 180 - ori = cor)

5. If you form a triangle on each quadrant (Now look at the black lines),  As you know, we can find cos sin tan on every right angle triangle using adjacent, opposite and hypotenuse lines. Because original angle is more than 90 degrees, we only find the cos sin tan for corresponding angle.
SOHCAHTOA

cos = adj/hyp              sin = opp/hyp              tan = opp/adj

Notice that in any of your quadrants, adjacent line falls on x-axis, and opposite line falls on y-axis.
Ok, so now we are finding VALUES of cos sin tan in EVERY quadrant.

In quadrant I, both x-axis and y-axis are positive, and hypotenuse is positive everywhere (Pythagoras Theorem, even if  'a' or 'b' is negative, after square is positive, so 'c' is positive)
So cos is +x/1 = + value. ('x' because adj falls on + x-axis line, so we use +x)
sin is +y/1 = + value
tan = +x/+y = +
So in first quadrant, ALL positive

Repeat for every quadrant, you will get:
Quadrant II: cos tan -, sin +
Quadrant III: cos sin -, tan +
Quadrant IV: sin tan -, cos +

If you summarize from Quadrant I to IV, it is ALL, SIN, TAN, COS positive
So use this to make them rmb: All Scientist Talk Crap, OR All Science Teacher Crazy (Not Science Tutor ar! Later Science Dpt have war with us liao LOL)

So this is the first thing that we can get from unit circle. Second thing is, how to find the trigonometric value of an angle, given the coordinates?

Refer to the first diagram again.

 Can you find value of the angle "teta" given that (x, y) is (0.6, 0.8)?
Rmb just now we say adj = x, opp = y. So now adj = 0.6 units, opp = 0.8 units.
So we can use any of cos sin tan to find teta (I will put teta as O for now)
tan O = opp/adj
tan O = 0.8/0.6
tan O = 1.33333333
O = 'shift' tan 1.33333 (use calculator, IMPOSSIBLE to use your brain)
O = 53.13 degrees

Very easy right? Now lets use harder examples.

First thing to do:
1. Determine coordinates, quadrant, and in that quadrant, sin cos tan which is positive.
2. Work out solutions

1. Coordinates of Q are (-0.5, -0.87). In Quadrant III, tan is positive, sin cos are negative.
2. sin O is opp/hyp, = y/1
    sin O = -0.87 = D

Now, can you find WHAT is ANGLE O?
sin O = -0.87
If you follow the workings in the previous example. You will not get your answer.
O = 'shift' sin -0.87
O = - 60.46???? (NEGATIVE?) negative actually means turn in the terbalik way, means instead from quadrant I x-axis turn anticlockwise, we turn clockwise 60.46 degree. That will bring us into Quadrant IV, but the answer isn't correct either, we should be in Quadrant III. HOW!!!????

So this is the limit of calculator. Because sin O = -0.87 GOT TWO ANSWERS. one falls in Quadrant III, one in Quadrant IV. (All Scientist Talk Crap, sin is negative in Quadrant III and IV). Calculator can only show one answer. So students always panic, cannot get answer.

So now the trick is, use CORRESPONDING ANGLE APPROACH.
So now, take away the negative sign. Let sin O = 0.87. In these questions, tell students that negative or positive is just INDICATOR to tell you whr the quadrant is.

sin O = 0.87
O = 'shift' sin 0.87 = 60.46

Now you know that the corresponding angle is 60.46, how to convert to original angle?

In Quadrant III, ori angle = 180 + corresponding angle
Therefore, The angle that we want is 180 + 60.46 = 240.46.
So we found the answer, dont need to use the 'negative' sign at all. So must tell them, when press calculator, DONT input NEGATIVE, or else confuse themselves only. (of course if you are pro, know the theory super superbly well, can work de, but I myself oso tend to get confuse so I dont recommend input negative)

So typical exam question is like this de:

WALAO A! WTHBBQOMG

In these questions, things to do:
1. Put all the info given in place
2. Determine whether to use ori angle or corresponding angle. (99.9% use corresponding de la, whr got test ori so easy de?)
3. Determine the relationship between ori and corr angle, and find the quadrant
4. Find out in the quadrant, sin cos tan which is positive and negative
5. Work out solutions.

1. cos x = 3/5, means adj/hyp is 6/10. Hence AC is 10cm, and BC will be 8cm.

2. We need to find y. y is greater than 90 degree. So we use corresponding angle to help us to find original angle.

3. Whr is corresponding angle???? you can see that y is outside the triangle. The angle ACB (next to y) should be corr angle. Means corr + y = 180. 180 degree is in which quadrant? In quadrant II lo. (90 to 180, dun take 180 to 270)

4. In Quadrant II, sin positive, tan cos negative

5. We are finding TAN y. Tan y = - tan (angle ACB) <------- see the negative? Cause' in quadrant II, corresponding tan is negative.
tan (angle ACB) = opp/adj
tan (angle ACB) = 6/8
tan (angle ACB) = 3/4
tan y = - tan (angle ACB)
tan y = - 3/4 = C

So you can try to find angle y also. ;)

Answer: 143.13 degree

YAY NOW WE FINISH 1st part. Still got special angles and graph OMGWTFBBQMCB.

Special angles actually is derived from 2 types of triangles.
To see how to derive, see http://sk19math.blogspot.com/2007/05/special-angles-in-trigonometry.html

You can combine the sin cos tan to see a clearer picture. I will upload last year notes for your info. the notes oso got how to derive but very simple version, and got give you a list of the angles

Part III, graph. See the notes la LOL
1. In their syllabus, only 0 to 360 degree. they only need to know sin x, cos x, and tan x graph. If they ask got -sin x ar, sin -x etc etc ar, tell them NO, that is in Add Maths, and say "i think u are in wrong class u can go AM class now" lol
***** But 2005 they got ask sin 2x. But i dunno why, cause' shouldn't ask de. If sin 2x, the graph basically becomes

If sin x goes up and down within 360 degree, sin2x goes up down up down.
If sinx = 1, x is 90
If sin 2x = 1, x is 45 lo. (Sin 2(45) = 1), so at your x-axis, sin 2(180) = sin 360, and sin 2(360) = sin 720. Means if you have sin2x graph, you basically draw sin x graph twice. You pick few points then try to plot la then I think u understand de.

2. Their careless mistake: Example,

Most of them will choose A. Because they just look at the shape of the graph then put. So dikenakan dy. They din check the x-axis. x-axis is until 180 only. Because for A, the x-axis should be until 360 degree. So 180 degree should be half part of the graph only. Answer is C

Thats all you need to know for Trigo. Walao A...I think my longest post ever.


Thats all la. Signing off noobiak. Paiseh 2nd part 3rd part very rush cause going out for wedding dinner jor.

some tips in teaching form 2 cirlces

mathematical reasoning part 2 (argument)

as last week i teach wrongly on Compound statement.**
after finding out the true meaning of CS. CS comes from combination of a statement AND / OR a statement. IN OPERATION type question.

Argument
separated in to 3 types of argument. Every argument comes with a General Statement, that provides all information to you.

Note : General Statement is definitely a true statement, no need to reconsider the truth of the statement.

Type 1 (2 Premise and 1 Conclusion)
Premise 1: ALL something IS/HAVE/ARE/HAS something. (general statement)
Premise 2: C IS something.
Conclusion: C IS something. 

Type 2 (2 Implication and 1 Conclusion)
Implication 1: IF something THEN something. (general statement)

Implication 2: something IS TRUE.
Conclusion: C is something IS TRUE.

Type 3 (2 Implication and 1 Conclusion)
Premise 1: IF something THEN something. (general statement)

Premise 2: something IS NOT TRUE.
Conclusion: something IS NOT TRUE. (FIXED)


SPECIFIC TO GENERAL (INDUCTION) GENERALIZATION : THE Nth TERM IS N^2+N, WHERE N=1,2,3,...

GENERAL TO SPECIFIC (DEDUCTION) CONCLUSION : AT LEAST IN THE RANGE.
2=1^2+1
6=2^2+2
12=3^2+3

mathematical reasoning. - LJ version

excluding Argument.
i discuss this with my students.
STATEMENT
no question element inside, no directive element inside, pure sentence based that leads your decision to TRUE or FALSE.

after learning this, it's further explained by the following subtopics.
-Quanlifier
further explain with question on determining what is the meaning of "ALL" and "SOME".
-Operation
further explain with question on determining what is the difference of using "or" and "and".
-Implication
i explained if ..."antecedent"..., then ... "consequent"...
i use example on:
Bryan is a boy
Bryan has a dick
i make it a implication based sentence.
IF Bryan is a boy, THEN Bryan has a dick.
i further make explain my Converse an implication as "if Bryan has a dick, then he is a boy."
the main thing that happens here is the meaning and the STATEMENT's truth doesn't change, it's still a TRUE statement.
Since the implication and the Converse implication is TRUE and doesn't change it's original meaning. then we can combined the two statement into a COMPOUND STATEMENT... like this:-
Bryan is a boy if and only if he has a dick.
then i stopped. and say i will teach them argument next week. and revise SETS.
BTW, i write out a separate paper with very basic Mathematical reasoning questions.

statistic form 3, how to teach ??

my answer is.
first, this chapter seperate into 2 diff subtopics.
1. pie chart question.
2.analysing data question.

pie chart
what is do was, i tell them a scenario.
im now analysis a school, finding out the percentage of student who go to school by what type of transport.
jet-50
walk-15
car-20
fly with hands-80

now find me the percentage.
so what i do is, i will total up the number and get 165 students in the school. later to find each of it i will take the total number 165 stud. divide by the amount i need, later multiply by 100% and i will get the percentage for each type of transportation.

hence, can u see that im using a Universally applicable formulae which tell us.

the amount you need (car/jet/walk/fly)   x   100 %  
total amount
= percentage for each sector.

then we will get the answer.
how if i wanna convert into angle format which the total is 360 degree ? u understand now ?

after this, i will enter into analysis question.

analysing data question
i further explain this into 2 diff types of question.
which is called the DATA question and TABLE question.

after telling them what is data and what is TABLE type question, we let them know what is Mode, Mean and Median.
Mode = highest Frequency
Mean = Average/Purata...just like your school report. total up the marks of 8 subjects then total marks divide by 8 subjects.
Median = middle of all data, after rearranging it into ascending order.

Types of Questions please refer our maths form 3 notes.
analysing data question.
we will have a table right ?
let them see this thing.
after u complete in explaining MEAN table type question.
u rub of one of the frequecy.

for example.
    score x        1     2     3     4
frequency y     4     3     1     6

mean we will total up xy then divide by total y right ?
then find the answer. this MEAN will be  2.5.

now RUB of the 6. and replace by x
Hint given, Means is 2.5. find x
this is what they dunno. =)


Gud luck in teaching. amithaba.

Linear Equation form 2. Share this with u all.

“Linear” Algebraic term is known as Terms with ONE TYPE unknown attached to the co-efficient only. (Unknown has to be in POWER ONE)
For Example: 3x, 4y, 1/3 a
Let say I have 3xy, 4wx, or1/3 ab^2, we will have more than one type of unknown. They are Non-Linear Algebraic Terms.
Hence, if we have 3x+6y, this will be known as a Linear Algebraic Expression. Refer Practice 1.
So, what we need to know now is…what is Expression ???
Like what we mentioned in our February Note’s content page, Expression is known as a question with no definite answer, we are just simplifying the question because without equal to SOMETHING we can’t solve our unknowns. We will simplify it.
If it’s known as an Equation, therefore we will have equals to SOMETHING. We will solve it, and get the value of the unknown.
For instance, 3x+6y, 4x+2, 3a+4b-c (Expression)
3x+2=6, 5y-5z=12 (Equation)
Since our chapter 4 is Linear Equation, therefore we solve it and get the value of the unknown. Refer Example 1,2.
But our Chapter covers only Linear Equation with ONE UNKNOWN. 

seterusnya...
Learn Linear Equation like kinder garden standard
Still remember how we do +2=5, =?
Being a clever Math student during primary, we know that the bracket equals to 3, but how we find the answer ????
We need to use Linear Equation Concept.
So what is Linear Equation Concept?
Remember this forever and vegetable!!
As long as when you move a symbol over an EQUAL, your symbol will change.