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Math Help - Radian Measure

  1. #1
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    Radian Measure

    My teacher gave me some notes on Radian Measure and I don't quiet understand a few things.
    (Numbers are in Degrees)
    When the teacher wrote converting Degrees to Radian, vice versa, here is something I am quite confused.

    Convert to Radian
    30 = 30 x Pi (factor) 180 = Pi (factor) 6

    A question like that I understand, because 180/30 = 6.
    But, a question like this I am confused


    120 = 120 x Pi (factor) 180 = 2Pi (factor) 3

    Now this is where I am confused. Where does the 2Pi and the 3 come from?
    120/180 = 1.5... 3 is the double of 1.5. Is the the 2 in 2Pi that makes it 3?
    I do not understand how the teacher got to this answer, can someone please help me explain in more detail. Thank you very much =D
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  2. #2
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    Re: Radian Measure

    Your teacher cancelled a factor of 60 from the division

    \dfrac{120}{180} = \dfrac{2 \times 60}{3 \times 60} = \dfrac{2}{3}


    nb: please use "/" without the quotation marks to mean division, factor is used to mean something completely different!
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  3. #3
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    Re: Radian Measure

    Hello, viviboy!

    Your use of the word "factor" is baffling.
    I suspect you meant "fraction".
    (But I don't know why you didn't simply type: Pi/6)


    My teacher gave me some notes on Radian Measure.

    My teacher wrote:

    Convert to Radian
    30^o \;=\; 30^o \times \frac{\pi}{180^o} \:=\: \frac{\pi}{6}

    A question like that I understand, because 180/30 = 6.

    But, a question like this I am confused

    . . 120^o \;=\; 120^o \times \frac{\pi}{180^o} \:=\:\frac{2\pi}{3}

    Now this is where I am confused.
    Where does the 2Pi and the 3 come from? .From the multiplication!

    I doubt that your teacher wrote it that way.
    If so, he/she should be brought up on charges.

    Would your teacher add: . \tfrac{1}{3} + \tfrac{1}{2} .like this?

    1 \text{ (factor) }3 \:+\: 1\text{ (factor) }2 \;=\;2\text{(factor) }6 \:+\: 3\text{ (factor) }6 \;=\;5\text{ (factor) }6


    Wow! . . . That's new one!

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  4. #4
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    Re: Radian Measure

    Oh sorry! I meant fraction...what was I thinking back there?
    The teacher was actually converting Degrees to Radians, which I think I did say that.
    And I somewhat understand what e^(i*pi) was trying to say. You basically find a "common factor" =P (I hope i used that word right this time) between 120 and 180.
    So if a number was to be, say 225. My answer would be 4Pi/3 .
    Is there a faster way to find the answer? Because what I'm doing is just punching in 225/2,/3,/4 and so on till I find a common factor between the two numbers.

    Also when converting radians back to degrees how you would do so?
    Such as this question.
    5Pi/6 - the answer is 150 degrees
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  5. #5
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    Re: Radian Measure

    The only way to do this is to do it right.
    By definition one radian is the measure of any angle that subtends an arc of length the same as the radius if the circle.
    So a straight central angle contains a diameter. That is it subtends a semi-circle in that has length \pi\cdot r, where r is the radius of the circle. Thus, in a circle radius 1 a straight angle has degree measure of 180^o and radian measure  \pi so one radian is \left(\dfrac{180}{\pi}\right)^o.

    THUS \dfrac{5\pi}{6}\cdot\left(\dfrac{180}{\pi}\right)^  o=\left(150\right)^o.
    Last edited by Plato; July 16th 2011 at 02:42 PM.
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  6. #6
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    Re: Radian Measure

    Thank you for helping me =D.

    I've found an easier way for me to find the answer to the conversions.

    For degree - radian, I put #/180. And I get the fraction of it, which is the radian.

    For radian - degree I put #x180 div denominator. And I get the degree of it.

    Now I have another question, which would probably be my last.

    When converting radian - degree, how would I convert a radian which is in decimal?
    (Ex. 4.2 Rad) or (Ex. .2 Rad)
    The teacher never taught us that, but it is in our homework. ><
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  7. #7
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    Re: Radian Measure

    Quote Originally Posted by viviboy View Post
    Thank you for helping me =D.

    I've found an easier way for me to find the answer to the conversions.

    For degree - radian, I put #/180. And I get the fraction of it, which is the radian.

    For radian - degree I put #x180 div denominator. And I get the degree of it.

    Now I have another question, which would probably be my last.

    When converting radian - degree, how would I convert a radian which is in decimal?
    (Ex. 4.2 Rad) or (Ex. .2 Rad)
    The teacher never taught us that, but it is in our homework. ><
    why does it matter if the value of radians is a decimal?

    do it the same way ... (radians) \times \frac{180}{\pi} \, = \, (degrees)
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  8. #8
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    Re: Radian Measure

    Oh! I guess I overthought that question, or because it was written differently from my other questions I got stump by it. Thank you!
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