# Thread: Converting between degrees and radians

1. ## Converting between degrees and radians

We have been here before on this subject in the past.

I understand if I wish to convert radians to degrees then (pi) / (180) x angle in degrees = angle in radians.

I also understand that if I wish to convert angles in degrees to radians, then (180) / (pi) x angle in radians = angle in degrees.

I have also seen angles in radians shown as (pi) / (6) = 30 degrees.

Now if this information is presented to me (pi) / (6) x 57.3 = 30 degrees.

If I wanted to change 30 degrees to radians, then using the above method I can do the conversions, but here is where I loose the understanding?

If I do a conversion, say I want to convert 270 degrees to radians, then by the following method;

angle in radians = (pi) / (180) x 270 = 4.71 radians

How do I convert the decimal 4.71 radians to the proper conversion (3 pi) / (2)

so 270 degrees = (3 pi) / (2) radians

2. ## Re: Converting between degrees and radians

Originally Posted by David Green
We have been here before on this subject in the past.

I understand if I wish to convert radians to degrees then (pi) / (180) x angle in degrees = angle in radians.

I also understand that if I wish to convert angles in degrees to radians, then (180) / (pi) x angle in radians = angle in degrees.

I have also seen angles in radians shown as (pi) / (6) = 30 degrees.

Now if this information is presented to me (pi) / (6) x 57.3 = 30 degrees.

If I wanted to change 30 degrees to radians, then using the above method I can do the conversions, but here is where I loose the understanding?

If I do a conversion, say I want to convert 270 degrees to radians, then by the following method;

angle in radians = (pi) / (180) x 270 = 4.71 radians

How do I convert the decimal 4.71 radians to the proper conversion (3 pi) / (2)

so 270 degrees = (3 pi) / (2) radians
Forget the decimal points and leave your answers in terms of $\pi$ to avoid rounding errors.

As you say $\theta ^c = \dfrac{\pi^c}{180^o} \cdot 270^o = \dfrac{270\pi}{180}$ but note that you can cancel out a factor of 90 to get $\theta = \dfrac{3\pi}{2}$

3. ## Re: Converting between degrees and radians

Originally Posted by e^(i*pi)
Forget the decimal points and leave your answers in terms of $\pi$ to avoid rounding errors.

As you say $\theta ^c = \dfrac{\pi^c}{180^o} \cdot 270^o = \dfrac{270\pi}{180}$ but note that you can cancel out a factor of 90 to get $\theta = \dfrac{3\pi}{2}$
Not sure if this is the right way to explain it, but here goes;

270(pi) / 180 = 3 x 90 = 270, thus 270 - 90 = 180. Now subtract 90 from the denominator 180 and this equates to 2.

so now we have 180 / 90 = 2

and 3 x 90 = 270, so;

3(pi) / 2 is the result.

4. ## Re: Converting between degrees and radians

Originally Posted by David Green
Not sure if this is the right way to explain it, but here goes;

270(pi) / 180 = 3 x 90 = 270, thus 270 - 90 = 180. Now subtract 90 from the denominator 180 and this equates to 2.

so now we have 180 / 90 = 2

and 3 x 90 = 270, so;

3(pi) / 2 is the result.
I've never come across that method before and I can't quote follow it although it seems like you're complicating matters

I would say it as $\dfrac{270\pi}{180} = \dfrac{3 \cdot 90 \cdot \pi}{2 \cdot 90}$ and since we have 90 on top and on bottom we cancel it.