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Simple way to translate degrees into radians?

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    I'm doing edexcel c2 and have a table showing angles in degrees and radians, but the table is big and I won't have it in the exam. East way to convert degrees into radians anyone, and vice versa?
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    Degrees to radians: multiply by \dfrac{\pi}{180}
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    Why do you need to convert between them?

    Just know that \pi = 180^o
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    Into Radians: Number of degrees x  \frac{\pi}{180^o}.

    Into Degrees: Number of radians x  \frac{180^o}{\pi}.
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    (Original post by EierVonSatan)
    Why do you need to convert between them?

    Just know that \pi = 180^o
    On the exam they can ask you to convert an angle you have found into radians.
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    The brain-dead calculator method is:

    \text{degrees} = \text{radians} \times \dfrac{180}{\pi}

    \text{radians} = \text{degrees} \times \dfrac{\pi}{180}

    The way to remember this is that 180^{\circ} = \pi\ \text{rad} (which you should know anyway) so you need to multiply by \dfrac{180}{\pi} or \dfrac{\pi}{180}. To decide which one, it's fairly obvious that 180 is a lot bigger than \pi, and any given angle is represented by 'more degrees than radians', so to go from radians to degrees you multiply by the top-heavy fraction, and to go from degrees to radians you multiply by the bottom-heavy fraction.

    For most angles this brain-dead "hammer the calculator" method isn't very useful and you certainly won't learn much from it. But you should remember that 2\pi represents a full circle, so you can work out the conversions by taking appropriate fractions of this. For instance 90° is a quarter of a circle, and so it is \dfrac{2\pi}{4} = \dfrac{\pi}{2} radians. And 30° is a twelfth of a circle, so it is \dfrac{2\pi}{12} = \dfrac{\pi}{6} radians. And so on.
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    (Original post by nuodai)
    The brain-dead calculator method is:

    \text{degrees} = \text{radians} \times \dfrac{180}{\pi}
    \text{radians} = \text{degrees} \times \dfrac{\pi}{180}
    The way to remember this is that 180^{\circ} = \pi\ \text{rad} (which you should know anyway) so you need to multiply by \dfrac{180}{\pi} or \dfrac{\pi}{180}. To decide which one, it's fairly obvious that 180 is a lot bigger than \pi, and any given angle is represented by 'more degrees than radians', so to go from radians to degrees you multiply by the top-heavy fraction, and to go from degrees to radians you multiply by the bottom-heavy fraction.

    For most angles this brain-dead "hammer the calculator" method isn't very useful and you certainly won't learn much from it. But you should remember that 2\pi represents a full circle, so you can work out the conversions by taking appropriate fractions of this. For instance 90° is a quarter of a circle, and so it is \dfrac{2\pi}{4} = \dfrac{\pi}{2} radians. And 30° is a twelfth of a circle, so it is \dfrac{2\pi}{12} = \dfrac{\pi}{6} radians. And so on.
    Oh thanks that makes so much sense now! I think my teacher tried explaining it like that but kind of failed.

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Updated: April 16, 2012
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