radian & degree & a trick

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    Radian & Degree & A Trick

    Prepared by LENG KIEN YUEN

    14 July 2011

    1

    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

    2

    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?