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Math Help - Radians to degrees and vica/versa

  1. #1
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    Radians to degrees and vica/versa

    This is for understanding purposes only.

    The basics are;

    one radian is the angle subtended at the centre of a circle by an arc that is the same length as the radius. From this a person can find the number of radians in a full turn, i.e. 360 degrees.

    But what if you only wanted to find the number of radians for any given number of degrees less than 360 degrees?

    I am a bit at a loss here because I have a table of worked values, but they don't cover every number of degrees between 0 and 360?

    Also the table of values and all data previous to it does not give any example how the conversion has been completed, i.e

    30 degrees = pi/6
    3.141 / 6 = 0.52

    To me something is missing, they do not balance?

    Can anyone advise what is missing please.

    Thanks

    David

    Found the solution to the problem,

    3.141 / 6 = 0.52 x 57.2 = 30 degrees.

    The above works for any number of degrees between 0 and 360
    Last edited by David Green; September 11th 2011 at 12:56 PM. Reason: found the solution to the problem
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  2. #2
    Member anonimnystefy's Avatar
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    Re: Radians to degrees and vica/versa

    hi DG

    you already know that 360 deg converts to 2*pi rad.now if you wanted to convert alpha deg to rad,then you can use proportion. 360 to 2*pi is like alpha to beta where beta is alpha converted to rad.

    so you get 360: (2*pi)=alpha:beta.

    cross multiply to get 360 deg*beta=2*pi*alpha

    dividing by 360deg you get: beta=(pi*alpha)/180deg

    this is the actual formula for the conversion,so if you put in 30 deg for alpha you will get pi/6.nothin missin,everythin in its place.
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  3. #3
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    Re: Radians to degrees and vica/versa

    Quote Originally Posted by David Green View Post
    One radian is the angle subtended at the centre of a circle by an arc that is the same length as the radius. From this a person can find the number of radians in a full turn, i.e. 360 degrees.
    But what if you only wanted to find the number of radians for any given number of degrees less than 360 degrees?
    360^o\sim 2\pi that read "360 degrees corresponds to two pi".

    So 180^0\sim 1\pi,~90^o\sim \frac{\pi}{2}~\&~1^0\sim \frac{\pi}{180}~.

    Thus 63^0\sim \frac{63\pi}{180}~.
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