Hey! Sign in to get help with your study questionsNew here? Join for free to post

Simple way to translate degrees into radians?

Announcements Posted on
AQA GCSE physics P1 unofficial mark scheme 05-05-2016
  1. Offline

    ReputationRep:
    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?
  2. Offline

    ReputationRep:
    Degrees to radians: multiply by \dfrac{\pi}{180}
  3. Offline

    ReputationRep:
    Why do you need to convert between them?

    Just know that \pi = 180^o
  4. Offline

    ReputationRep:
    Into Radians: Number of degrees x  \frac{\pi}{180^o}.

    Into Degrees: Number of radians x  \frac{180^o}{\pi}.
  5. Offline

    ReputationRep:
    (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.
  6. Offline

    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.
  7. Offline

    ReputationRep:
    (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.

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. Oops, you need to agree to our Ts&Cs to register
  2. Slide to join now Processing…

Updated: April 16, 2012
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

Today on TSR

AQA GCSE maths

Check the unofficial mark scheme

Poll
What date is the EU referendum on?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read here first

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups
Study resources
Quick reply
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.