radian & degree & a trick
TRANSCRIPT
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8/6/2019 Radian & Degree & a Trick
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Radian & Degree & A Trick
Prepared by LENG KIEN YUEN
14 July 2011
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Radian & Degree ()
Radian is another way in expressing degree. It is useful in circular measurement and trigonometry.
where is a irrational number and 3.14159265358979...
and
Note
Radian, and degree, are SI unit. The unit is cancelled when divided with the same unit. It is same aswhat we learned in the first chapter in Physics. In Wikipedia, Radian is the ratio between the length of an arc and its
radius. Hence, the radian is a pure number that needs no unit
symbol, and in mathematical writing the symbol is almost
always omitted.
In the absence of any symbol radians are assumed, and when degreesare meant the symbol is used. Please take note! (Now, I only knew
this fact! Paiseh Paiseh)
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Radian & Degree & A Trick
Prepared by LENG KIEN YUEN
14 July 2011
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Little Trick (Very useful in Mathematics and Physics)
You may come across some questions like 1 apples for RM 2. How much
should be paid for 2 apple?
It is a easy question, answer is RM 4 ( 2 RM2 ).
Then, if 2 apples for RM 3, then how much should be paid for 5 apples?
It is slightly difficult.
Approach 1
Conventional approach is finding the price per apple then multiply with
number of apple bought. That is
.
Where
. is value per apple.
Approach 2
What is the proportion of 5 apples to 2 apples?
5 apples is
. times of 2 apples.
So, the price of 5 apple is . .
If you combine the steps together, then you will have the following
.
Note:
These 2 approaches are only working when the a variable is directlyproportional to another variable and can be expressed in this form
y is dependant variable (Output), x is independent variable (Input) and k is a constant (Fixed) For example, , Priceis dependant variable
and Number of apples is independent variable.
where k is Price per apples(Constant).
It also means that if we double the number of apples, we also doublethe price.
It also works for ,
, and many more as we just need to
treat whole
and
as a independent variable.
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Radian & Degree & A Trick
Prepared by LENG KIEN YUEN
14 July 2011
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My Thought
From the example above, you may think that I justslightly alter theorientation of the equation but actually they are determined by 2
different thoughts. It is interesting? Which suit you the most? It may sound simple and stupid. Yet, it is very useful in Mathematics
and Physics.
It has link with linear equation when c = 0. With this trick, I can handle a lot of questions with similar type!
Little Extra / Extension of Knowledge (I discovered it during STPM)
In circular measurement, area of a segment is given
. What is the
area in term of A with the radius is
and is doubled?