First, I took 180 (which has a corresponding radian of just π) and divided it by 5, because the angles increase by 5 degrees. 1 could have divided the degree (times π) by 180 but you would always have to reduce. 180/5 is equal to 36. This is how I knew that the denominator for every radian would be 36. I then took the degree that I was finding the radian for, and divided that by 5 -- because what is done to one side should be done to the other. The resulting number is the numerator for the fraction.
Here's an example of my work when finding the radian for 30°:
Step 1: divide 180° by 5 to reduce (360° is double 180° -- and the radians are 2π and π, respectively-- this is why dividing into 360 is unnecessary, because 180 is a easier degree to reduce from)
180°/5° = 36
Step 2: Divide 30° by 5 because you divided 180 by 5.
30°/5=6°
Step 3: 36 is the "universal" denominator, because the circle increases by 5 consistently and we are converting all the degrees to radians.
6°/36°
Step 4: Reduce the fraction and don't forget the numerator is multiplied by π (since we are dealing with a circle)
6 is common factor of 6 and 36. Finally answer is---> π/6
This is how all the radian conversions were completed, I also used an online calculator to check all of my conversions.
http://www.mattdoyle.net/old/raddeg.html
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