Is the Circle Division Math for the Stator Correct?

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The discussion centers on verifying the math for dividing a circle into nine equal parts, as presented on a specific website. The author questions the use of \sin20° in the calculations, suggesting that \sin40° should be used instead. They provide an alternative approach using the formula for the chord length, which aligns with the results from the website. The author expresses uncertainty about their trigonometric understanding and seeks clarification on the correct methodology. The accuracy of the math is crucial for their potential project involving this division.
MacLaddy
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Not a homework question, I was just hoping someone could assist me with understanding some math. Actually, more accurately, I was wondering if someone could double check the math on the following website.

http://www.otherpower.com/statormold.shtml

If you scroll down you will see some explanations on how to accurately divide the circle into nine equal parts, but I believe he is doing it incorrectly. See where the "Sides, Angles, and Sines" paper is shown. Seems odd that he would be using the \sin20\deg when it is 40\deg.

Wouldn't you just do the following

\frac{\pi12}{9}~=~4.188...

Thanks for any input you can offer. I have been considering taking up this project, but if the math is wrong I may not...
 
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Well, I digress. I realized that I needed to figure out the "chord" for the angle, as it will not follow the arc. So I used the formula c~=~r\sqrt{2-2cos40}. That gave the same answer that he was coming up with by just multiplying \sin20~by~12.

I apologize if I posted this in the wrong section, it just seemed appropriate here due to the subject matter.

Apparently I'm missing something in my trig knowledge.
 
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