How do you convert the angle in radians to degrees when pi is on the side of the fraction rather than in the fraction?
Good question. I think I know what you mean, but I’m not completely sure. Let me know if this isn’t what you meant.
Let’s imagine a certain angle in radians. We’ll call it (4pi/3).
We know that because multiplication is commutative (a x b = b x a) that (4pi/3) = (4/3)pi. The angle in radians, whether pi is located outside of the fraction or inside of the fraction, is the same value.
If we want to find out what the radian angle is in degrees, we can set up a proportionality that will ensure we won’t get the answer wrong. I will solve for the angle in degrees using the example radian angle I mentioned earlier. This is how we do it:
Pi radians = 180 degrees.
(4/3)*pi radians = (4/3)*180 degrees
(4pi/3) radians = 240 degrees.
There is your answer. I hope it is what you needed. Replace (4/3) with whatever fraction you have instead, and set up the proportionality exactly the same. All you need to remember is that pi = 180 degrees.