# Thread: Radians to degrees and vica/versa

1. ## 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

2. ## 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.

3. ## Re: Radians to degrees and vica/versa

Originally Posted by David Green
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?
$\displaystyle 360^o\sim 2\pi$ that read "360 degrees corresponds to two pi".

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

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