Hopefully this can help you as it has helped me.
Let's cut the circle in half and recapitulate:
Alright, so, we already know that the denominators go like this:
6, 4, 3, 2, 3, 4, 6. We also know that the numerators starting from the positive x-axis all the way to the 90° angle are always π. If you too have problems remembering what numerators come after the 90° angle, I think I have come up with a trick. I'll try my best to explain.
Hopefully you've noticed the pattern too.
Every time my teacher asks me to find the radians in the 2nd quadrant (as shown) counter-clockwise, I just say to myself: "2,3,3,4,5,6" and fill in the blanks.
But that's not all!
The pattern goes even further!
We've just added 7,6,5,4,4,3,3,2.
I find this long pattern easier to remember than the 17 radians, haha!
2,3,3,4,5,6,7,6,5,4,4,3,3,2.
Notice that if we split this pattern like this:
2,3,3,4,5,6 (7) and
6,5,4,4,3,3,2,
they're almost, what I like to call, "inversely-identical," except for the extra four.
Now, for the fourth quadrant, I have a different approach.
Actually, I've come up with a "temporary" formula to help you learn those tricky numbers:
n = 2d - 1
This formula will automatically give you the coefficient of π!
Hopefully this will clear up your B17 problems. It sure did for me! :)
And if you still don't understand, or want to know another trick, here it is!
Good heavens, you must have put a LOT of hours into this, Joey! Are you sure you want to be a police office, and not a math teacher? :) You seem to have a real love of explaining things....that's how I got hooked! Your system is brilliant, mathematically sound, and most importantly, it works for you. I am sure it will help others, not to mention inspire others to come up with their own system AND share it as well. In colour. On their blog. Thanks again!
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