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I was not trying to teach trigonometry in this video, hence why I did not explain why we use arc tangent. We use (arc) tangent because it uses the triangle ratio of O/A (opposite side over adjacent side). This is convenient because those are literally the values we have in the positional vector (X & Y). Other ratios require H (hypotenuse) - which are completely viable ways to calculate these angles as well.
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Shout out to Chris for the thumbnail ⭐